This equates the marginal rate of substitution (the consumer”s internal valuation) with the price Ratio (the market’s valuation). Solving for x x x P x P_x P x individual demand curve x = d i ( P x ) x = d_i(P_x) x = d i ( P x )
At each price, we add up the quantities demanded by all consumers.
## 2. Supply
Horizontal summation of individual firm supply curves.
The price mechanism is the process by which prices adjust to equate demand and supply, thereby Allocating resources without central direction. It performs three functions:
(arc elasticity) formula: $\mathrm{PED} = \frac{\Delta Q}{\Delta P} \times \frac{(P_1 + P_2)/2}{(Q_1 + Q_2)/2}$. CIE Uses the point elasticity formula. Check your board's preference.Problem 1. A consumer has utility U ( x , y ) = x 0.5 y 0.5 U(x, y) = x^{0.5}y^{0.5} U ( x , y ) = x 0.5 y 0.5 M = 100 M = 100 M = 100 P x = 4 P_x = 4 P x = 4 P y = 2 P_y = 2 P y = 2 x x x y y y x x x P x P_x P x
Hint Set up MRS = price ratio: $\frac{y}{x} = \frac{P_x}{P_y} = 2$So $y = 2x$. Substitute into budget constraint: $4x + 2(2x) = 100 \Rightarrow 8x = 100 \Rightarrow x = 12.5$$y = 25$. General demand: $x = \frac{M}{2P_x}$$y = \frac{M}{2P_y}$. At $P_x = 5$: $x = 10$.Problem 2. The market demand for good X X X Q D = 100 − 2 P Q_D = 100 - 2P Q D = 100 − 2 P Q S = 20 + 3 P Q_S = 20 + 3P Q S = 20 + 3 P
Hint $100 - 2P = 20 + 3P \Rightarrow 80 = 5P \Rightarrow P^* = 16$$Q^* = 68$. CS = $\int_0^{68} [50 - Q/2 - 16] \, dQ = \int_0^{68} [34 - Q/2] \, dQ = [34Q - Q^2/4]_0^{68} = 2312 - 1156 = 1156$. PS = $\int_0^{68} [16 - (Q - 20)/3] \, dQ = \int_0^{68} [22/3 - Q/3] \, dQ = [22Q/3 - Q^2/6]_0^{68} = 498.67 - 770.67 = \ldots$ Recalculate: inverse supply $P = (Q - 20)/3 + 0 = (Q-20)/3$. PS = $\int_0^{68} [16 - (Q-20)/3] dQ = \int_0^{68} [16 - Q/3 + 20/3] dQ = \int_0^{68} [68/3 - Q/3] dQ = [68Q/3 - Q^2/6]_0^{68} = 1541.33 - 770.67 = 770.67$.Problem 3. A linear demand curve passes through points ( P , Q ) = ( 10 , 50 ) (P, Q) = (10, 50) ( P , Q ) = ( 10 , 50 ) ( P , Q ) = ( 20 , 30 ) (P, Q) = (20, 30) ( P , Q ) = ( 20 , 30 ) ∣ P E D ∣ = 1 |\mathrm{PED}| = 1 ∣ PED ∣ = 1
Hint Demand equation: slope $= \frac{30-50}{20-10} = -2$So $Q = 70 - 2P$. At $(10, 50)$: PED $= \frac{10}{50} \times (-2) = -0.4$ (inelastic). At $(20, 30)$: PED $= \frac{20}{30} \times (-2) = -1.33$ (elastic). Midpoint: $Q = 35$$P = 17.5$: PED $= \frac{17.5}{35} \times (-2) = -1$.Problem 4. The price of good A A A B B B A A A B B B
Hint Using midpoint formula: XED $= \frac{(80-100)/90}{(7-5)/6} = \frac{-20/90}{2/6} = \frac{-0.222}{0.333} = -0.667$. Since XED < 0, $A$ and $B$ are complements. The magnitude (0.667) suggests a moderate complement relationship.Problem 5. A government imposes a specific tax of £3 per unit on a good with demand Q D = 120 − P Q_D = 120 - P Q D = 120 − P Q S = 2 P − 30 Q_S = 2P - 30 Q S = 2 P − 30
Hint With tax, supply shifts up: $P_s = P_d - 3$So $Q_S = 2(P_d - 3) - 30 = 2P_d - 36$. New equilibrium: $120 - P_d = 2P_d - 36 \Rightarrow 156 = 3P_d \Rightarrow P_d = 52$. $P_s = 49$. $Q^* = 68$. Tax burden on consumers: $52 - 50 = 2$ (out of £3). Tax burden on producers: $50 - 49 = 1$. DWL $= \frac{1}{2} \times 3 \times (70 - 68) = 3$.Problem 6. Prove that if demand is perfectly inelastic (P E D = 0 \mathrm{PED} = 0 PED = 0
Hint With vertical demand curve, quantity doesn't change. The price consumers pay rises by the full amount of the tax. With horizontal demand curve, consumers are willing to pay only $P^*$. Producers must absorb the entire tax to continue selling.Problem 7. A firm’s total cost function is T C = 50 + 10 Q + 0.5 Q 2 TC = 50 + 10Q + 0.5Q^2 T C = 50 + 10 Q + 0.5 Q 2
Hint $MC = dTC/dQ = 10 + Q$. Supply curve: $P = MC$ for $P \geq AVC$. $AVC = 10 + 0.5Q$$\min AVC = 10$ at $Q = 0$. So supply: $Q = P - 10$ for $P \geq 10$. At $P = 25$: $Q = 15$.Problem 8. “A firm should always produce at the level where total revenue is maximised.” Evaluate this statement.
Hint False. A profit-maximising firm produces where $MR = MC$Not where $TR$ is maximised ($MR = 0$). Since $MC \gt 0$ (), the profit-maximising output is lower than the revenue-maximising output. Only if $MC = 0$ would the two coincide.Problem 9. When the price of cinema tickets rises from £8 to £10, weekly attendance falls from 500 to 400. Calculate PED. If the cinema raises prices further to £12, and PED remains constant, Predict the new attendance. Is this assumption realistic?
Hint PED $= \frac{-100/450}{2/9} = \frac{-0.222}{0.222} = -1$ (unit elastic, using midpoints). If PED remains $-1$: $\frac{\%\Delta Q}{\%\Delta P} = -1$. Price rises from 10 to 12 = 20%. So quantity falls by 20%: $Q = 400 \times 0.8 = 320$. The assumption is unrealistic because PED varies along a linear demand curve.Problem 10. The government is considering imposing a tax on cigarettes. Using demand and supply Analysis, discuss the likely effects on (a) equilibrium price and quantity, (b) consumer surplus, (c) tax revenue, and (d) deadweight loss. In your evaluation, consider the implications of inelastic Demand for tax revenue vs the goal of reducing smoking.
Hint Cigarettes have inelastic demand (few substitutes, addictive). (a) Price rises substantially, quantity falls modestly. (b) Consumer surplus falls by a large amount (consumers bear most of the tax burden). (c) Tax revenue is high because quantity doesn't fall much. (d) DWL is relatively small (narrow triangle). Evaluation: if the goal is revenue, inelastic goods are ideal for taxation. If the goal is reducing smoking, the tax may be insufficient — complementary policies (education, regulation) may be needed.Problem 11. Two goods have demand curves Q A = 50 − P A + 0.5 P B Q_A = 50 - P_A + 0.5P_B Q A = 50 − P A + 0.5 P B Q B = 80 − 2 P B + P A Q_B = 80 - 2P_B + P_A Q B = 80 − 2 P B + P A B B B A A A P_A = 20$$P_B = 10 .
Hint $\mathrm{XED}_{BA} = \frac{\partial Q_B / \partial P_A \times P_A}{Q_B}$. $\partial Q_B / \partial P_A = 1$. At $P_A = 20$$P_B = 10$: $Q_B = 80 - 20 + 20 = 80$. XED $= 1 \times 20/80 = 0.25$. Positive, so $A$ and $B$ are weak substitutes.Problem 12. Evaluate the usefulness of elasticity concepts for government policymakers. In your Answer, discuss the limitations of elasticity estimates in practice.
Hint Useful for: tax policy (tax inelastic goods for revenue), subsidy design, price regulation. Limitations: estimates vary with time period and data quality, assume ceteris paribus, may change after policy intervention (endogeneity), difficult to estimate for new goods.Example. Market demand is Q D = 200 − 4 P Q_D = 200 - 4P Q D = 200 − 4 P Q S = 20 + 6 P Q_S = 20 + 6P Q S = 20 + 6 P
Answer. Set Q D = Q S Q_D = Q_S Q D = Q S 200 − 4 P = 20 + 6 P ⟹ 180 = 10 P ⟹ P ∗ = 18 200 - 4P = 20 + 6P \implies 180 = 10P \implies P^* = 18 200 − 4 P = 20 + 6 P ⟹ 180 = 10 P ⟹ P ∗ = 18
Q ∗ = 200 − 4 ( 18 ) = 200 − 72 = 128 Q^* = 200 - 4(18) = 200 - 72 = 128 Q ∗ = 200 − 4 ( 18 ) = 200 − 72 = 128
Stability check. At P = 20 > P ∗ P = 20 \gt P^* P = 20 > P ∗ Q_D = 120$$Q_S = 140 . Excess supply of 20 20 20 ⟹ \implies ⟹ P = 15 < P ∗ P = 15 \lt P^* P = 15 < P ∗ Q_D = 140$$Q_S = 110 . Excess demand of 30 30 30 ⟹ \implies ⟹ □ \square □
When both curves shift simultaneously, the effect on equilibrium price is ambiguous unless we know The relative magnitudes.
Demand Shift Supply Shift Effect on P ∗ P^* P ∗ Effect on Q ∗ Q^* Q ∗ Right (increase) Right (increase) Ambiguous Increases Right (increase) Left (decrease) Increases Ambiguous Left (decrease) Right (increase) Decreases Ambiguous Left (decrease) Left (decrease) Ambiguous Decreases
Example. Demand increases and supply decreases simultaneously. Both shifts push price up, so P ∗ P^* P ∗
Example. “The price of coffee rises. Explain the effect on the market for tea.”
Correct analysis. Coffee and tea are substitutes (X E D > 0 \mathrm{XED} \gt 0 XED > 0 right (increase in demand for tea). At the Original price, there is now excess demand for tea. The price of tea rises, and the quantity of tea Traded increases. This is a shift in the demand curve, not a movement along it.
Incorrect analysis. “The price of tea rises, so demand for tea falls.” This confuses a movement Along the curve with a shift.
Scenario Correct Terminology Curve Effect Price of the good itself changes Change in quantity demanded/supplied Movement along the curve Any other determinant changes Change in demand/supply Shift of the curve
Example. Demand: Q D = 100 − 2 P Q_D = 100 - 2P Q D = 100 − 2 P Q S = 10 + 3 P Q_S = 10 + 3P Q S = 10 + 3 P
Answer. Equilibrium: 100 - 2P = 10 + 3P \implies 90 = 5P \implies P^* = 18$$Q^* = 64 .
Inverse demand: P = 50 − Q / 2 P = 50 - Q/2 P = 50 − Q /2 = 50 = 50 = 50 P = ( Q − 10 ) / 3 P = (Q - 10)/3 P = ( Q − 10 ) /3
C S = ∫ 0 64 [ 50 − Q / 2 − 18 ] d Q = ∫ 0 64 [ 32 − Q / 2 ] d Q = [ 32 Q − Q 2 / 4 ] 0 64 = 2048 − 1024 = 1024 CS = \int_0^{64} [50 - Q/2 - 18]\,dQ = \int_0^{64} [32 - Q/2]\,dQ = [32Q - Q^2/4]_0^{64} = 2048 - 1024 = 1024 C S = ∫ 0 64 [ 50 − Q /2 − 18 ] d Q = ∫ 0 64 [ 32 − Q /2 ] d Q = [ 32 Q − Q 2 /4 ] 0 64 = 2048 − 1024 = 1024
P S = ∫ 0 64 [ 18 − ( Q − 10 ) / 3 ] d Q = ∫ 0 64 [ 64 / 3 − Q / 3 ] d Q = [ 64 Q / 3 − Q 2 / 6 ] 0 64 = 1365.3 − 682.7 = 682.7 PS = \int_0^{64} [18 - (Q - 10)/3]\,dQ = \int_0^{64} [64/3 - Q/3]\,dQ = [64Q/3 - Q^2/6]_0^{64} = 1365.3 - 682.7 = 682.7 P S = ∫ 0 64 [ 18 − ( Q − 10 ) /3 ] d Q = ∫ 0 64 [ 64/3 − Q /3 ] d Q = [ 64 Q /3 − Q 2 /6 ] 0 64 = 1365.3 − 682.7 = 682.7
Total surplus = 1024 + 682.7 = 1706.7 = 1024 + 682.7 = 1706.7 = 1024 + 682.7 = 1706.7
A binding price ceiling set below P ∗ P^* P ∗
The distribution of a tax burden between consumers and producers depends on the relative price Elasticities of demand and supply:
B u r d e n o n c o n s u m e r s B u r d e n o n p r o d u c e r s = ∣ P E S ∣ ∣ P E D ∣ \frac{\mathrm{Burden on consumers}}{\mathrm{Burden on producers}} = \frac{|\mathrm{PES}|}{|\mathrm{PED}|} Burdenonproducers Burdenonconsumers = ∣ PED ∣ ∣ PES ∣
The more inelastic side bears a greater share of the tax burden.
Example. Demand: Q D = 150 − P Q_D = 150 - P Q D = 150 − P Q S = 2 P − 30 Q_S = 2P - 30 Q S = 2 P − 30 t = 10 t = 10 t = 10
Answer. Original equilibrium: 150 − P = 2 P − 30 ⟹ P ∗ = 60 150 - P = 2P - 30 \implies P^* = 60 150 − P = 2 P − 30 ⟹ P ∗ = 60 Q ∗ = 90 Q^* = 90 Q ∗ = 90
With tax, supply shifts: P s = P d − 10 P_s = P_d - 10 P s = P d − 10 Q S = 2 ( P d − 10 ) − 30 = 2 P d − 50 Q_S = 2(P_d - 10) - 30 = 2P_d - 50 Q S = 2 ( P d − 10 ) − 30 = 2 P d − 50
New equilibrium: 150 − P d = 2 P d − 50 ⟹ 200 = 3 P d ⟹ P d = 66.67 150 - P_d = 2P_d - 50 \implies 200 = 3P_d \implies P_d = 66.67 150 − P d = 2 P d − 50 ⟹ 200 = 3 P d ⟹ P d = 66.67
P s = 56.67 P_s = 56.67 P s = 56.67 Q ∗ = 83.3 Q^* = 83.3 Q ∗ = 83.3
Consumer burden: 66.67 − 60 = 6.67 66.67 - 60 = 6.67 66.67 − 60 = 6.67 60 − 56.67 = 3.33 60 - 56.67 = 3.33 60 − 56.67 = 3.33
Ratio: 6.67 / 3.33 = 2 6.67/3.33 = 2 6.67/3.33 = 2 ∣ P E S ∣ = ( d Q S / d P ) ( P / Q ) = 2 ( 60 / 90 ) = 1.33 |\mathrm{PES}| = (dQ_S/dP)(P/Q) = 2(60/90) = 1.33 ∣ PES ∣ = ( d Q S / d P ) ( P / Q ) = 2 ( 60/90 ) = 1.33 ∣ P E D ∣ = ( d Q D / d P ) ( P / Q ) = ∣ − 1 ∣ ( 60 / 90 ) = 0.67 |\mathrm{PED}| = (dQ_D/dP)(P/Q) = |-1|(60/90) = 0.67 ∣ PED ∣ = ( d Q D / d P ) ( P / Q ) = ∣ − 1∣ ( 60/90 ) = 0.67 = 1.33 / 0.67 = 2 = 1.33/0.67 = 2 = 1.33/0.67 = 2 □ \square □
Deadweight loss: D W L = 1 2 × t × Δ Q = 1 2 × 10 × ( 90 − 83.3 ) = 33.5 \mathrm{DWL} = \frac{1}{2} \times t \times \Delta Q = \frac{1}{2} \times 10 \times (90 - 83.3) = 33.5 DWL = 2 1 × t × Δ Q = 2 1 × 10 × ( 90 − 83.3 ) = 33.5
Example. When average income rises from £ 30 000 £30\,000 £30 000 £ 33 000 £33\,000 £33 000
Answer. Bus travel: YED = ( 475 − 500 ) / 487.5 ( 33000 − 30000 ) / 31500 = − 0.0513 0.0952 = − 0.54 = \frac{(475-500)/487.5}{(33000-30000)/31500} = \frac{-0.0513}{0.0952} = -0.54 = ( 33000 − 30000 ) /31500 ( 475 − 500 ) /487.5 = 0.0952 − 0.0513 = − 0.54 ⟹ \implies ⟹
Foreign holidays: YED = ( 230 − 200 ) / 215 0.0952 = 0.1395 0.0952 = 1.47 = \frac{(230-200)/215}{0.0952} = \frac{0.1395}{0.0952} = 1.47 = 0.0952 ( 230 − 200 ) /215 = 0.0952 0.1395 = 1.47 > 1 \gt 1 > 1 ⟹ \implies ⟹
If XED between two firms’ products is high (close substitutes), they operate in the same market and A merger between them would significantly reduce competition. Competition authorities use XED to Define the relevant market .
Confusing “demand” with “quantity demanded.” “Demand” refers to the entire curve; “quantity demanded” refers to a specific point on the curve. A price change causes a change in quantity demanded (movement), not a change in demand (shift).
Ignoring the ceteris paribus assumption. In reality, multiple factors change simultaneously. When analysing a change, state what is being held constant.
Assuming elastic demand always means less revenue. The relationship between PED and revenue depends on the direction of the price change. A price decrease with elastic demand increases revenue; a price increase with elastic demand decreases revenue.
Misapplying the midpoint formula. The midpoint (arc elasticity) formula gives the elasticity at the midpoint of the change, not at either endpoint. For precise analysis, use point elasticity.
Forgetting that supply can be elastic or inelastic too. PES determines how quickly producers can respond to price changes. In the short run, supply is less elastic than in the long run.
Assuming tax burden depends on who pays the government. The legal incidence (who writes the cheque) does not determine the economic incidence (who bears the burden). The burden depends on relative elasticities.
Problem 1. Market demand is Q D = 80 − P Q_D = 80 - P Q D = 80 − P Q S = 2 P − 20 Q_S = 2P - 20 Q S = 2 P − 20 20 20 20 P ∗ P^* P ∗ Q ∗ Q^* Q ∗
Hint Original: $80 - P = 2P - 20 \implies P^* = 33.3$$Q^* = 46.7$. New demand: $Q_D' = 100 - P$. New equilibrium: $100 - P = 2P - 20 \implies P^* = 40$$Q^* = 60$. $\Delta P^* = 6.7$$\Delta Q^* = 13.3$.Problem 2. A good has PED = − 0.4 = -0.4 = − 0.4
Hint $\%\Delta Q_d = \mathrm{PED} \times \%\Delta P = -0.4 \times 10 = -4\%$. Quantity falls by 4%. Since $|\mathrm{PED}| \lt 1$ (inelastic), revenue rises. New $TR = 1.10P \times 0.96Q = 1.056PQ$. Revenue increases by 5.6%.Problem 3. The government imposes a £ 5 £5 £5 Q D = 100 − P Q_D = 100 - P Q D = 100 − P Q S = 3 P − 20 Q_S = 3P - 20 Q S = 3 P − 20
Hint Original: $P^* = 30$$Q^* = 70$. With tax: $Q_S = 3(P_d - 5) - 20 = 3P_d - 35$. New: $100 - P_d = 3P_d - 35 \implies P_d = 33.75$. $P_s = 28.75$. $Q^* = 66.25$. Consumer burden: $3.75$Producer burden: $1.25$. Ratio $= 3$. DWL $= \frac{1}{2} \times 5 \times 3.75 = 9.375$.Problem 4. A consumer spends £ 200 £200 £200 X X X £ 10 £10 £10 £ 12 £12 £12
Hint Original quantity $= 200/10 = 20$. PED (midpoint) $= \frac{(15-20)/17.5}{(12-10)/11} = \frac{-0.286}{0.182} = -1.57$. $|\mathrm{PED}| \gt 1$So demand is elastic.Problem 5. Demand for electric cars is Q D = 50 + 0.5 Y − 3 P Q_D = 50 + 0.5Y - 3P Q D = 50 + 0.5 Y − 3 P Y Y Y Y = 40 Y = 40 Y = 40 P = 8 P = 8 P = 8 44 44 44
Hint At $Y = 40, P = 8$: $Q_D = 50 + 20 - 24 = 46$. YED $= (\partial Q_D/\partial Y)(Y/Q_D) = 0.5 \times 40/46 = 0.435$ (normal necessity). PED $= (\partial Q_D/\partial P)(P/Q_D) = -3 \times 8/46 = -0.522$ (inelastic). At $Y = 44$: $Q_D = 50 + 22 - 24 = 48$. Increase of 2 units.Problem 6. “A subsidy on a good with elastic demand and inelastic supply will benefit consumers More than producers.” Evaluate this statement using tax incidence analysis.
Hint The benefit of a subsidy is distributed in the same way as a tax burden: the more inelastic side receives more benefit. With elastic demand (consumers can switch) and inelastic supply (producers cannot exit), producers receive a larger share of the subsidy benefit. The statement is incorrect: producers benefit more. The price consumers pay falls by less than the price producers receive increases.Income elasticity of demand is critical for understanding how different sectors perform during the business cycle:
Cyclical goods (YED > 1): demand rises more than proportionally during booms and falls more during recessions. Examples: luxury cars, foreign holidays, restaurant meals, airline travel. These sectors experience amplified fluctuations.
Defensive goods (0 < YED < 1): demand is relatively stable across the cycle. Examples: food, utilities, basic healthcare, public transport. These sectors are less affected by recessions.
Inferior goods (YED < 0): demand rises during recessions and falls during booms. Examples: discount retailers, instant noodles, public transport. These sectors may be counter-cyclical.
Worked example. During the 2008-09 recession, UK GDP fell by 6%. Using YED estimates:
Restaurant demand (YED = 1.5): falls by 1.5 × 6 % = 9 % 1.5 \times 6\% = 9\% 1.5 × 6% = 9% Supermarket food demand (YED = 0.3): falls by 0.3 × 6 % = 1.8 % 0.3 \times 6\% = 1.8\% 0.3 × 6% = 1.8% Discount retailer demand (YED = -0.5): rises by 0.5 × 6 % = 3 % 0.5 \times 6\% = 3\% 0.5 × 6% = 3% This explains why budget retailers (Aldi, Lidl) grew during the recession while upmarket restaurants suffered.
Cross-price elasticity is used by competition authorities to define the relevant market:
Worked example. The CMA is investigating a merger between two coffee shop chains. XED between the two chains’ products is estimated at 1.8 (strong substitutes). XED between the chains and independent coffee shops is 0.3 (weak substitutes). XED between the chains and tea shops is 0.1 (very weak substitutes).
The high XED (1.8) between the two chains suggests they operate in the same relevant market. The merger would significantly reduce competition. The CMA might block the merger or require remedies (selling some stores).
The low XED with tea shops (0.1) suggests they are not close substitutes and should not be included in the relevant market definition.
Worked example with linear demand. A firm faces demand Q = 100 − 2 P Q = 100 - 2P Q = 100 − 2 P
Inverse demand: P = 50 − Q / 2 P = 50 - Q/2 P = 50 − Q /2 T R = 50 Q − Q 2 / 2 TR = 50Q - Q^2/2 T R = 50 Q − Q 2 /2
PED at different points: At Q = 25 , P = 37.50 Q = 25, P = 37.50 Q = 25 , P = 37.50 = ( 37.5 / 25 ) × ( − 2 ) = − 3.0 = (37.5/25) \times (-2) = -3.0 = ( 37.5/25 ) × ( − 2 ) = − 3.0 Q = 50 , P = 25 Q = 50, P = 25 Q = 50 , P = 25 = ( 25 / 50 ) × ( − 2 ) = − 1.0 = (25/50) \times (-2) = -1.0 = ( 25/50 ) × ( − 2 ) = − 1.0 Q = 75 , P = 12.50 Q = 75, P = 12.50 Q = 75 , P = 12.50 = ( 12.5 / 75 ) × ( − 2 ) = − 0.33 = (12.5/75) \times (-2) = -0.33 = ( 12.5/75 ) × ( − 2 ) = − 0.33
TR at different points: T R ( 25 ) = 50 ( 25 ) − 625 = 625 TR(25) = 50(25) - 625 = 625 T R ( 25 ) = 50 ( 25 ) − 625 = 625 T R ( 50 ) = 50 ( 50 ) − 1250 = 1250 TR(50) = 50(50) - 1250 = 1250 T R ( 50 ) = 50 ( 50 ) − 1250 = 1250 T R ( 75 ) = 50 ( 75 ) − 2812.5 = 937.50 TR(75) = 50(75) - 2812.5 = 937.50 T R ( 75 ) = 50 ( 75 ) − 2812.5 = 937.50
This confirms: TR is maximised where ∣ PED ∣ = 1 |\text{PED}| = 1 ∣ PED ∣ = 1
Question 1 (12 marks). The government imposes a specific tax of GBP 8 per unit on a good with demand Q D = 200 − 4 P Q_D = 200 - 4P Q D = 200 − 4 P Q S = 4 P − 40 Q_S = 4P - 40 Q S = 4 P − 40
Full Mark Scheme **(a) New equilibrium (4 marks).** Original equilibrium: $200 - 4P = 4P - 40 \Rightarrow 240 = 8P \Rightarrow P^* = 30$$Q^* = 80$.With tax: supply shifts to Q S = 4 ( P d − 8 ) − 40 = 4 P d − 72 Q_S = 4(P_d - 8) - 40 = 4P_d - 72 Q S = 4 ( P d − 8 ) − 40 = 4 P d − 72 200 - 4P_d = 4P_d - 72 \Rightarrow 272 = 8P_d \Rightarrow P_d = 34$$Q = 64 . P s = 34 − 8 = 26 P_s = 34 - 8 = 26 P s = 34 − 8 = 26
(b) Tax incidence (4 marks). Consumer burden: P d − P ∗ = 34 − 30 = GBP 4 P_d - P^* = 34 - 30 = \text{GBP } 4 P d − P ∗ = 34 − 30 = GBP 4 P ∗ − P s = 30 − 26 = GBP 4 P^* - P_s = 30 - 26 = \text{GBP } 4 P ∗ − P s = 30 − 26 = GBP 4 1 : 1 1:1 1 : 1
(c) Deadweight loss (4 marks). DWL = 1 2 × t × Δ Q = 1 2 × 8 × ( 80 − 64 ) = 1 2 × 8 × 16 = GBP 64 \text{DWL} = \frac{1}{2} \times t \times \Delta Q = \frac{1}{2} \times 8 \times (80 - 64) = \frac{1}{2} \times 8 \times 16 = \text{GBP } 64 DWL = 2 1 × t × Δ Q = 2 1 × 8 × ( 80 − 64 ) = 2 1 × 8 × 16 = GBP 64
Question 2 (25 marks). “The price mechanism is the most effective method of resource allocation in a market economy.” Evaluate this statement.
Full Mark Scheme **Arguments for the price mechanism (10 marks):** - Signalling: prices convey information about scarcity, quality, and consumer preferences. High prices signal high demand or scarce supply, incentivising production and conservation. - Incentive: the profit motive drives firms to produce efficiently (minimise costs) and innovate (develop new products). - Rationing: prices allocate goods to those willing and able to pay the most, which () maximises total surplus. - Adam Smith's "invisible hand": individuals pursuing self-interest are led, as if by an invisible hand, to promote the social interest. - First Theorem of Welfare Economics: competitive equilibrium is Pareto efficient (maximises total surplus).Arguments against / limitations (10 marks):
Market failure: externalities, public goods, information asymmetry, and market power cause the price mechanism to misallocate resources. Equity concerns: the price mechanism allocates based on willingness to pay, which reflects income/wealth, not need or merit. Essential goods (healthcare, education) may be under-consumed by the poor. Short-run price rigidity: menu costs, contracts, and imperfect information cause prices to adjust slowly, leading to persistent disequilibrium. Public goods: the price mechanism cannot provide non-excludable, non-rivalrous goods because the free-rider problem prevents payment. Externalities: the price mechanism ignores external costs and benefits. Pollution is under-priced; education is under-consumed. Behavioural factors: consumers and firms may not be rational (prospect theory, bounded rationality, framing effects). Evaluation (5 marks):
The price mechanism is highly effective for allocating most goods and services in a market economy but is NOT the most effective method for ALL types of goods. For private goods in competitive markets, the price mechanism is superior to central planning (as demonstrated by the collapse of command economies). For public goods, merit goods, and goods with significant externalities, the price mechanism fails and government intervention is needed. The best approach is a mixed economy: the price mechanism for most allocation, supplemented by government intervention to correct market failures and address equity concerns. Conclusion: the statement is too absolute. The price mechanism is the most effective method for ALLOCATIVE EFFICIENCY but not for EQUITY or the provision of public goods. Question 3 (12 marks). A government is considering imposing a maximum price (price ceiling) of GBP 5 on a good with demand Q D = 100 − 8 P Q_D = 100 - 8P Q D = 100 − 8 P Q S = 4 P − 20 Q_S = 4P - 20 Q S = 4 P − 20
Full Mark Scheme **(a) Shortage (4 marks).** At $P_c = 5$: $Q_D = 100 - 8(5) = 60$$Q_S = 4(5) - 20 = 0$. The supply is zero at $P = 5$ (below the supply curve intercept of $P = 5$ where $Q_S = 0$). Actually, supply intercept: $4P - 20 = 0 \Rightarrow P = 5$. So $Q_S = 0$ at the ceiling price. Shortage $= 60 - 0 = 60$ units. The market completely dries up.Wait, let me reconsider. The supply curve Q S = 4 P − 20 Q_S = 4P - 20 Q S = 4 P − 20 P = 5 P = 5 P = 5 P_c = 5$$Q_S = 0 . This means the price ceiling is set exactly at the supply intercept, so the market ceases to function.
For a more interesting case, set P c = 7 P_c = 7 P c = 7 Q_D = 100 - 8(7) = 44$$Q_S = 4(7) - 20 = 8 . Shortage = 44 − 8 = 36 = 44 - 8 = 36 = 44 − 8 = 36
(b) Change in consumer surplus (4 marks). Original CS: at P^* = 10$$Q^* = 100 - 80 = 20 . Choke price = 100 / 8 = 12.5 = 100/8 = 12.5 = 100/8 = 12.5 CS o r i g = ∫ 0 20 [ ( 12.5 − Q / 8 ) − 10 ] d Q = ∫ 0 20 [ 2.5 − Q / 8 ] d Q = [ 2.5 Q − Q 2 / 16 ] 0 20 = 50 − 25 = 25 \text{CS}_{orig} = \int_0^{20} [(12.5 - Q/8) - 10]\,dQ = \int_0^{20} [2.5 - Q/8]\,dQ = [2.5Q - Q^2/16]_0^{20} = 50 - 25 = 25 CS or i g = ∫ 0 20 [( 12.5 − Q /8 ) − 10 ] d Q = ∫ 0 20 [ 2.5 − Q /8 ] d Q = [ 2.5 Q − Q 2 /16 ] 0 20 = 50 − 25 = 25
New CS (at P c = 7 P_c = 7 P c = 7 = 8 = 8 = 8 P c = 7 P_c = 7 P c = 7 P c = 7 P_c = 7 P c = 7 Q = 0 Q = 0 Q = 0 8 8 8 ∫ 0 8 [ ( 12.5 − Q / 8 ) − 7 ] d Q = ∫ 0 8 [ 5.5 − Q / 8 ] d Q = [ 5.5 Q − Q 2 / 16 ] 0 8 = 44 − 4 = 40 \int_0^8 [(12.5 - Q/8) - 7]\,dQ = \int_0^8 [5.5 - Q/8]\,dQ = [5.5Q - Q^2/16]_0^8 = 44 - 4 = 40 ∫ 0 8 [( 12.5 − Q /8 ) − 7 ] d Q = ∫ 0 8 [ 5.5 − Q /8 ] d Q = [ 5.5 Q − Q 2 /16 ] 0 8 = 44 − 4 = 40
Change in CS: 40 − 25 = + 15 40 - 25 = +15 40 − 25 = + 15
(c) Evaluation (4 marks):
Consumers who obtain the good gain (CS increases from 25 to 40). Consumers who are excluded from the market lose (they would have bought at P = 10 P = 10 P = 10 P = 7 P = 7 P = 7 Non-price rationing: those who cannot buy may queue, pay bribes, or accept lower quality. These costs are not captured in the CS calculation. Producer surplus falls to zero (producers exit the market). DWL: 1 2 ( 10 − 7 ) ( 20 − 8 ) = 1 2 ( 3 ) ( 12 ) = 18 \frac{1}{2}(10 - 7)(20 - 8) = \frac{1}{2}(3)(12) = 18 2 1 ( 10 − 7 ) ( 20 − 8 ) = 2 1 ( 3 ) ( 12 ) = 18 Conclusion: the price ceiling benefits some consumers but harms others and creates a net welfare loss. The statement that it “benefits consumers” is misleading without qualification. Confusing “demand” with “quantity demanded.” “Demand” refers to the entire curve; “quantity demanded” refers to a specific point on the curve. A price change causes a movement along the curve (change in quantity demanded), not a shift of the curve (change in demand). This is the single most common exam error.
Applying the midpoint formula when point elasticity is asked for. The midpoint (arc elasticity) formula gives elasticity at the midpoint of a change, not at either endpoint. For precise analysis, use point elasticity. Always check which formula your exam board expects.
Assuming elastic demand always means less revenue. The relationship between PED and revenue depends on the direction of the price change. A price decrease with elastic demand increases revenue; a price increase with elastic demand decreases revenue.
Misapplying tax incidence. The legal incidence (who writes the cheque to the government) does not determine the economic incidence (who bears the burden). The burden depends on relative elasticities: the more inelastic side bears a greater share.
Forgetting that supply can be elastic or inelastic too. PES determines how quickly producers can respond to price changes. In the short run, supply is less elastic than in the long run. Always consider both demand and supply elasticities when analysing price changes.
Example. A consumer has a budget of GBP 100 to spend on food (F F F C C C P F = £ 5 P_F = \pounds 5 P F = £5 P C = £ 10 P_C = \pounds 10 P C = £10 U = F 0.5 C 0.5 U = F^{0.5}C^{0.5} U = F 0.5 C 0.5
Budget constraint: 5 F + 10 C = 100 ⇒ F = 20 − 2 C 5F + 10C = 100 \Rightarrow F = 20 - 2C 5 F + 10 C = 100 ⇒ F = 20 − 2 C
Optimal consumption: M R S = M U F / M U C = 0.5 F − 0.5 C 0.5 0.5 F 0.5 C − 0.5 = C / F MRS = MU_F/MU_C = \frac{0.5F^{-0.5}C^{0.5}}{0.5F^{0.5}C^{-0.5}} = C/F M R S = M U F / M U C = 0.5 F 0.5 C − 0.5 0.5 F − 0.5 C 0.5 = C / F
Set M R S = P F / P C MRS = P_F/P_C M R S = P F / P C C / F = 5 / 10 = 0.5 ⇒ C = 0.5 F C/F = 5/10 = 0.5 \Rightarrow C = 0.5F C / F = 5/10 = 0.5 ⇒ C = 0.5 F
Substitute into budget constraint: 5F + 10(0.5F) = 100 \Rightarrow 5F + 5F = 100 \Rightarrow F = 10$$C = 5 .
Utility: U = ( 10 ) 0.5 ( 5 ) 0.5 = 50 = 7.07 U = (10)^{0.5}(5)^{0.5} = \sqrt{50} = 7.07 U = ( 10 ) 0.5 ( 5 ) 0.5 = 50 = 7.07
Effect of a price change: Suppose P F P_F P F
New budget constraint: 8 F + 10 C = 100 ⇒ F = 12.5 − 1.25 C 8F + 10C = 100 \Rightarrow F = 12.5 - 1.25C 8 F + 10 C = 100 ⇒ F = 12.5 − 1.25 C M R S = P F / P C = 8 / 10 = 0.8 ⇒ C = 0.8 F MRS = P_F/P_C = 8/10 = 0.8 \Rightarrow C = 0.8F M R S = P F / P C = 8/10 = 0.8 ⇒ C = 0.8 F 8F + 10(0.8F) = 100 \Rightarrow 16F = 100 \Rightarrow F = 6.25$$C = 5 .
Substitution and income effects:
Substitution effect: holding utility constant at 7.07, the change in F F F C = 0.8 F C = 0.8F C = 0.8 F U = F 0.5 ( 0.8 F ) 0.5 = 0.8 F = 7.07 ⇒ F = 7.91 U = F^{0.5}(0.8F)^{0.5} = \sqrt{0.8}F = 7.07 \Rightarrow F = 7.91 U = F 0.5 ( 0.8 F ) 0.5 = 0.8 F = 7.07 ⇒ F = 7.91 F F F
Income effect: the price increase reduces real purchasing power. Income effect: F F F
Total effect: F F F
Since food is a normal good (income effect reinforces substitution effect), both effects work in the same direction: less food is consumed when the price rises.
Example. The EU Common Agricultural Policy (CAP) guarantees a minimum price for wheat. Demand: Q D = 500 − 2 P Q_D = 500 - 2P Q D = 500 − 2 P Q S = 3 P − 100 Q_S = 3P - 100 Q S = 3 P − 100 £ 120 \pounds 120 £120
Free market equilibrium: 500 - 2P = 3P - 100 \Rightarrow 600 = 5P \Rightarrow P = 120$$Q = 260 .
Interesting — the guaranteed price equals the market equilibrium price. Let me use a lower guaranteed price to make the example meaningful.
Actually, the guaranteed price is ABOVE the market equilibrium. Let me recalculate with the guaranteed price at 140.
Free market: P = 120$$Q = 260 (as above).
With price floor at 140: Q D = 500 − 280 = 220 Q_D = 500 - 280 = 220 Q D = 500 − 280 = 220 Q S = 420 − 100 = 320 Q_S = 420 - 100 = 320 Q S = 420 − 100 = 320 320 − 220 = 100 320 - 220 = 100 320 − 220 = 100
Cost to the government: 140 × 100 = £ 14 000 140 \times 100 = \pounds 14\,000 140 × 100 = £14 000
Welfare analysis: CS before: 1 2 ( 250 − 120 ) ( 260 ) = 16 900 \frac{1}{2}(250 - 120)(260) = 16\,900 2 1 ( 250 − 120 ) ( 260 ) = 16 900 Q = 0 ⇒ P = 250 Q = 0 \Rightarrow P = 250 Q = 0 ⇒ P = 250 1 2 ( 250 − 140 ) ( 220 ) = 12 100 \frac{1}{2}(250 - 140)(220) = 12\,100 2 1 ( 250 − 140 ) ( 220 ) = 12 100 − 4 800 -4\,800 − 4 800
PS before: 1 2 ( 120 − 33.33 ) ( 260 ) = 11 267 \frac{1}{2}(120 - 33.33)(260) = 11\,267 2 1 ( 120 − 33.33 ) ( 260 ) = 11 267 Q = 0 ⇒ P = 100 / 3 = 33.33 Q = 0 \Rightarrow P = 100/3 = 33.33 Q = 0 ⇒ P = 100/3 = 33.33 1 2 ( 140 − 33.33 ) ( 320 ) = 17 067 \frac{1}{2}(140 - 33.33)(320) = 17\,067 2 1 ( 140 − 33.33 ) ( 320 ) = 17 067 + 5 800 +5\,800 + 5 800
Government cost: 14,000. Net welfare change: − 4 800 + 5 800 − 14 000 = − 13 000 -4\,800 + 5\,800 - 14\,000 = -13\,000 − 4 800 + 5 800 − 14 000 = − 13 000
Deadweight loss: The price support creates DWL through two channels:
Overproduction: 320 − 260 = 60 320 - 260 = 60 320 − 260 = 60 = 1 2 ( 140 − 120 ) ( 60 ) = 600 = \frac{1}{2}(140 - 120)(60) = 600 = 2 1 ( 140 − 120 ) ( 60 ) = 600 Underconsumption: 260 − 220 = 40 260 - 220 = 40 260 − 220 = 40 = 1 2 ( 140 − 120 ) ( 40 ) = 400 = \frac{1}{2}(140 - 120)(40) = 400 = 2 1 ( 140 − 120 ) ( 40 ) = 400 = 1000 = 1000 = 1000 The remaining 12,000 of welfare loss is a pure transfer from taxpayers to producers (via government purchases). This is not a DWL per se, but it represents a redistribution that may be considered undesirable on equity grounds.
Example. The government imposes a tax on petrol. Petrol demand: Q P = 1000 − 5 P P Q_P = 1000 - 5P_P Q P = 1000 − 5 P P Q P = 4 P P − 200 Q_P = 4P_P - 200 Q P = 4 P P − 200 + 0.3 +0.3 + 0.3 Q E = 200 + 0.5 P P Q_E = 200 + 0.5P_P Q E = 200 + 0.5 P P
Initial petrol equilibrium: 1000 - 5P_P = 4P_P - 200 \Rightarrow 1200 = 9P_P \Rightarrow P_P = 133.33$$Q_P = 333.33 .
Tax of GBP 20 per litre on petrol: Q P = 4 ( P P − 20 ) − 200 = 4 P P − 280 Q_P = 4(P_P - 20) - 200 = 4P_P - 280 Q P = 4 ( P P − 20 ) − 200 = 4 P P − 280 1000 − 5 P P = 4 P P − 280 ⇒ 1280 = 9 P P ⇒ P P = 142.22 1000 - 5P_P = 4P_P - 280 \Rightarrow 1280 = 9P_P \Rightarrow P_P = 142.22 1000 − 5 P P = 4 P P − 280 ⇒ 1280 = 9 P P ⇒ P P = 142.22 142.22 − 20 = 122.22 142.22 - 20 = 122.22 142.22 − 20 = 122.22 Q P = 1000 − 5 ( 142.22 ) = 288.89 Q_P = 1000 - 5(142.22) = 288.89 Q P = 1000 − 5 ( 142.22 ) = 288.89
Effect on EVs: Petrol price rises from 133.33 to 142.22 (% Δ P P = ( 142.22 − 133.33 ) / 133.33 = 6.67 % \% \Delta P_P = (142.22 - 133.33)/133.33 = 6.67\% %Δ P P = ( 142.22 − 133.33 ) /133.33 = 6.67% % Δ Q E = X E D × % Δ P P = 0.3 × 6.67 = 2.0 % \% \Delta Q_E = XED \times \% \Delta P_P = 0.3 \times 6.67 = 2.0\% %Δ Q E = X E D × %Δ P P = 0.3 × 6.67 = 2.0%
Environmental benefit: If the average petrol car emits 120g/km of CO 2 \text{CO}_2 CO 2 CO 2 \text{CO}_2 CO 2 = 120 × 12000 / 10 6 = 1.44 = 120 \times 12000 / 10^6 = 1.44 = 120 × 12000/1 0 6 = 1.44
If 2% of the 333,333 car owners switch: 0.02 × 333 333 = 6 667 0.02 \times 333\,333 = 6\,667 0.02 × 333 333 = 6 667 CO 2 \text{CO}_2 CO 2 = 6 667 × 1.44 = 9 600 = 6\,667 \times 1.44 = 9\,600 = 6 667 × 1.44 = 9 600
Revenue and DWL: Tax revenue = 20 × 288.89 = 5 778 = 20 \times 288.89 = 5\,778 = 20 × 288.89 = 5 778 = 1 2 × 20 × ( 333.33 − 288.89 ) = 1 2 × 20 × 44.44 = 444.4 = \frac{1}{2} \times 20 \times (333.33 - 288.89) = \frac{1}{2} \times 20 \times 44.44 = 444.4 = 2 1 × 20 × ( 333.33 − 288.89 ) = 2 1 × 20 × 44.44 = 444.4
Net environmental benefit: If the social cost of carbon is GBP 50/tonne: 9 600 × 50 = 480 000 9\,600 \times 50 = 480\,000 9 600 × 50 = 480 000 = 480 000 − 444.4 = 479 556 = 480\,000 - 444.4 = 479\,556 = 480 000 − 444.4 = 479 556
Example. The government provides a production subsidy for solar panels. Demand: P = 5000 − 0.5 Q P = 5000 - 0.5Q P = 5000 − 0.5 Q P = 2000 + 0.3 Q P = 2000 + 0.3Q P = 2000 + 0.3 Q
Without subsidy: 5000 - 0.5Q = 2000 + 0.3Q \Rightarrow 3000 = 0.8Q \Rightarrow Q = 3750$$P = 3125 .
With subsidy: Supply shifts down: P = 1500 + 0.3 Q P = 1500 + 0.3Q P = 1500 + 0.3 Q 5000 − 0.5 Q = 1500 + 0.3 Q ⇒ 3500 = 0.8 Q ⇒ Q = 4375 5000 - 0.5Q = 1500 + 0.3Q \Rightarrow 3500 = 0.8Q \Rightarrow Q = 4375 5000 − 0.5 Q = 1500 + 0.3 Q ⇒ 3500 = 0.8 Q ⇒ Q = 4375
Consumer price: P c = 5000 − 0.5 ( 4375 ) = 2812.5 P_c = 5000 - 0.5(4375) = 2812.5 P c = 5000 − 0.5 ( 4375 ) = 2812.5 3125 − 2812.5 = 312.5 3125 - 2812.5 = 312.5 3125 − 2812.5 = 312.5 P p = 2812.5 + 500 = 3312.5 P_p = 2812.5 + 500 = 3312.5 P p = 2812.5 + 500 = 3312.5 3312.5 − 3125 = 187.5 3312.5 - 3125 = 187.5 3312.5 − 3125 = 187.5
Incidence: Consumer share = 312.5 / 500 = 62.5 % = 312.5/500 = 62.5\% = 312.5/500 = 62.5% = 187.5 / 500 = 37.5 % = 187.5/500 = 37.5\% = 187.5/500 = 37.5% P E D = − 0.5 × 3125 / 3750 = − 0.417 PED = -0.5 \times 3125/3750 = -0.417 P E D = − 0.5 × 3125/3750 = − 0.417 P E S = ( 1 / 0.3 ) × 3125 / 3750 = 2.78 PES = (1/0.3) \times 3125/3750 = 2.78 P E S = ( 1/0.3 ) × 3125/3750 = 2.78
Government cost: 500 × 4375 = 2 187 500 500 \times 4375 = 2\,187\,500 500 × 4375 = 2 187 500
Positive externality correction: If the marginal external benefit per solar panel is GBP 600 (reduced pollution, energy security): Social optimum: M S B = M P B + 500 MSB = MPB + 500 M S B = M P B + 500 5000 + 500 − 0.5 Q = 2000 + 0.3 Q ⇒ 3500 = 0.8 Q ⇒ Q = 4375 5000 + 500 - 0.5Q = 2000 + 0.3Q \Rightarrow 3500 = 0.8Q \Rightarrow Q = 4375 5000 + 500 − 0.5 Q = 2000 + 0.3 Q ⇒ 3500 = 0.8 Q ⇒ Q = 4375
The subsidy of GBP 500 achieves an output of 4375, which is close to (but not exactly) the social optimum of 4375. If the MEB were exactly 500, the subsidy would be perfectly set. In this case, the subsidy slightly under-corrects (optimal subsidy would be 600, not 500). The remaining DWL from under-correction: 1 2 ( 600 − 500 ) ( Q M E B = 600 ∗ − 4375 ) \frac{1}{2}(600 - 500)(Q^*_{MEB=600} - 4375) 2 1 ( 600 − 500 ) ( Q M E B = 600 ∗ − 4375 )
DWL of the subsidy (relative to the first-best): With MEB = 600 and subsidy = 500: the effective MPC becomes 2000 + 0.3 Q − 500 = 1500 + 0.3 Q 2000 + 0.3Q - 500 = 1500 + 0.3Q 2000 + 0.3 Q − 500 = 1500 + 0.3 Q 5000 − 0.5 Q + 600 = 5600 − 0.5 Q 5000 - 0.5Q + 600 = 5600 - 0.5Q 5000 − 0.5 Q + 600 = 5600 − 0.5 Q 5600 − 0.5 Q = 2000 + 0.3 Q ⇒ 3600 = 0.8 Q ⇒ Q ∗ = 4500 5600 - 0.5Q = 2000 + 0.3Q \Rightarrow 3600 = 0.8Q \Rightarrow Q^* = 4500 5600 − 0.5 Q = 2000 + 0.3 Q ⇒ 3600 = 0.8 Q ⇒ Q ∗ = 4500
The subsidy achieves Q = 4375 Q = 4375 Q = 4375 D W L = 1 2 ( M S B 4375 − M S C 4375 ) ( 4500 − 4375 ) DWL = \frac{1}{2}(MSB_{4375} - MSC_{4375})(4500 - 4375) D W L = 2 1 ( M S B 4375 − M S C 4375 ) ( 4500 − 4375 ) M S B 4375 = 5600 − 0.5 ( 4375 ) = 3412.5 MSB_{4375} = 5600 - 0.5(4375) = 3412.5 M S B 4375 = 5600 − 0.5 ( 4375 ) = 3412.5 M S C 4375 = 2000 + 0.3 ( 4375 ) = 3312.5 MSC_{4375} = 2000 + 0.3(4375) = 3312.5 M S C 4375 = 2000 + 0.3 ( 4375 ) = 3312.5 D W L = 1 2 ( 3412.5 − 3312.5 ) ( 125 ) = 1 2 ( 100 ) ( 125 ) = 6250 DWL = \frac{1}{2}(3412.5 - 3312.5)(125) = \frac{1}{2}(100)(125) = 6250 D W L = 2 1 ( 3412.5 − 3312.5 ) ( 125 ) = 2 1 ( 100 ) ( 125 ) = 6250
The subsidy is close to optimal but not perfect. A subsidy of GBP 600 would be first-best.
Example. The market for cigarettes has demand Q D = 200 − 4 P Q_D = 200 - 4P Q D = 200 − 4 P Q S = 6 P − 80 Q_S = 6P - 80 Q S = 6 P − 80
Step 1: Free market equilibrium. 200 - 4P = 6P - 80 \Rightarrow 280 = 10P \Rightarrow P = 28$$Q = 88 .
Step 2: With tax only. Q S = 6 ( P − 5 ) − 80 = 6 P − 110 Q_S = 6(P - 5) - 80 = 6P - 110 Q S = 6 ( P − 5 ) − 80 = 6 P − 110 200 − 4 P = 6 P − 110 ⇒ 310 = 10 P ⇒ P = 31 200 - 4P = 6P - 110 \Rightarrow 310 = 10P \Rightarrow P = 31 200 − 4 P = 6 P − 110 ⇒ 310 = 10 P ⇒ P = 31 Q = 200 − 124 = 76 Q = 200 - 124 = 76 Q = 200 − 124 = 76
Step 3: With tax AND price floor of 30. The price floor of 30 is BELOW the consumer price with tax (31), so the price floor is NOT binding. The equilibrium is the same as Step 2: P = 31$$Q = 76 .
If the price floor were 35: consumers pay 35. Q D = 200 − 140 = 60 Q_D = 200 - 140 = 60 Q D = 200 − 140 = 60 Q S Q_S Q S = 35 − 5 = 30 = 35 - 5 = 30 = 35 − 5 = 30 Q S = 6 ( 30 ) − 80 = 100 Q_S = 6(30) - 80 = 100 Q S = 6 ( 30 ) − 80 = 100 = 100 − 60 = 40 = 100 - 60 = 40 = 100 − 60 = 40 40 × 30 = 1200 40 \times 30 = 1200 40 × 30 = 1200
Step 4: With tax AND production quota of 40. The quota restricts supply to 40 units. At Q = 40 Q = 40 Q = 40 = P D = ( 200 − 40 ) / 4 = 40 = P_D = (200 - 40)/4 = 40 = P D = ( 200 − 40 ) /4 = 40 = P S = ( 40 + 80 ) / 6 = 20 = P_S = (40 + 80)/6 = 20 = P S = ( 40 + 80 ) /6 = 20 P S = P D − 5 = 35 P_S = P_D - 5 = 35 P S = P D − 5 = 35 P S P_S P S Q = 40 Q = 40 Q = 40
Actually, with the quota: supply is fixed at 40. The price is determined by demand: P D = 40 P_D = 40 P D = 40 40 − 5 = 35 40 - 5 = 35 40 − 5 = 35 35 − 20 = 15 35 - 20 = 15 35 − 20 = 15 = 15 × 40 = 600 = 15 \times 40 = 600 = 15 × 40 = 600
Combined effect: The quota (40) is more restrictive than the tax alone (76). The combined policy results in:
Higher consumer price (40 vs 31 with tax alone). Higher producer revenue per unit (35 vs 26 with tax alone). Lower quantity (40 vs 76). Quota rent of 600 (captured by whoever holds the quota rights). Tax revenue = 5 × 40 = 200 = 5 \times 40 = 200 = 5 × 40 = 200 5 × 76 = 380 5 \times 76 = 380 5 × 76 = 380 Total government revenue: tax revenue (200) + quota auction revenue (if quotas are auctioned, 600) = 800.
Welfare comparison:
Policy P consumer Q CS PS Govt revenue DWL None 28 88 968 361 0 0 Tax only 31 76 578 288 380 120 Tax + quota 40 40 100 400 + 600 200 560
The combined tax and quota is highly distortionary: DWL increases from 120 (tax only) to 560 (tax + quota). The quota is a blunt instrument that creates more DWL than the tax because it prevents the market from adjusting along the supply curve.
Example. The government establishes a buffer stock scheme for wheat. The target price is GBP 200 per tonne. Demand: Q D = 1000 − 2 P Q_D = 1000 - 2P Q D = 1000 − 2 P Q S = 3 P − 200 Q_S = 3P - 200 Q S = 3 P − 200
Free market equilibrium: 1000 - 2P = 3P - 200 \Rightarrow 1200 = 5P \Rightarrow P = 240$$Q = 520 .
Since the target price (200) is BELOW the market price (240), the buffer stock is irrelevant — the market price is already above the target. The government does not need to intervene.
If the target price is 280 (above market price): At P = 280 P = 280 P = 280 Q D = 1000 − 560 = 440 Q_D = 1000 - 560 = 440 Q D = 1000 − 560 = 440 Q S = 840 − 200 = 640 Q_S = 840 - 200 = 640 Q S = 840 − 200 = 640 = 640 − 440 = 200 = 640 - 440 = 200 = 640 − 440 = 200
Cost to government: 280 × 200 = 56 000 280 \times 200 = 56\,000 280 × 200 = 56 000 = 2000 = 2000 = 2000
If a bad harvest reduces supply: New supply Q S = 2 P − 100 Q_S = 2P - 100 Q S = 2 P − 100 1000 - 2P = 2P - 100 \Rightarrow 1100 = 4P \Rightarrow P = 275$$Q = 450 . The market price (275) is still below the target (280), so the government releases some stocks. Government releases: enough to push price to 280. At P = 280 P = 280 P = 280 Q_D = 440$$Q_S = 460 . Excess supply of 20. The government does NOT need to release stocks (supply exceeds demand even at the target price).
If supply falls further: Q S = P Q_S = P Q S = P 1000 - 2P = P \Rightarrow P = 333.33$$Q = 333.33 . Market price (333.33) is above target (280). The government sells stocks: Q_D(280) = 440$$Q_S(280) = 80 . Shortage = 360 = 360 = 360
Revenue from sales: 280 × 360 = 100 800 280 \times 360 = 100\,800 280 × 360 = 100 800
Buffer stock balance sheet:
Bought: 200 tonnes at 280 = 56,000. Sold: 360 tonnes at 280 = 100,800. Storage costs: 200 tonnes x 10/tonne x N years. Net profit: 100 800 − 56 000 − 2000 N = 44 800 − 2000 N 100\,800 - 56\,000 - 2000N = 44\,800 - 2000N 100 800 − 56 000 − 2000 N = 44 800 − 2000 N If stored for 5 years: net profit = 44 800 − 10 000 = 34 800 = 44\,800 - 10\,000 = 34\,800 = 44 800 − 10 000 = 34 800 = 0 = 0 = 0
Problems with buffer stock schemes:
Expensive: storage costs erode the profit margin. Market distortion: the target price sends the wrong signal to farmers (over-production). Quality deterioration: stored commodities may deteriorate. Political manipulation: governments may set the target price too high to win farmer votes. International trade: buffer stocks may conflict with WTO rules (they are a form of domestic support). EU Common Agricultural Policy (CAP): The EU operated a buffer stock scheme from the 1960s to the 1990s. By the 1980s, the “butter mountains” and “wine lakes” had become a political embarrassment. The scheme was reformed in 1992 (MacSharry reforms) and again in 2003, shifting from price support to direct income support for farmers.
Example. The government imposes a maximum rent of GBP 1,000/month on apartments. The free market rent is GBP 1,500/month. Demand: Q D = 2000 − P Q_D = 2000 - P Q D = 2000 − P Q S = P − 500 Q_S = P - 500 Q S = P − 500
Free market: 2000 - P = P - 500 \Rightarrow 2500 = 2P \Rightarrow P = 1250$$Q = 750 .
Wait, the free market rent is given as 1500 but the equilibrium gives 1250. Let me adjust the functions.
Demand: Q D = 3000 − P Q_D = 3000 - P Q D = 3000 − P Q S = P − 1500 Q_S = P - 1500 Q S = P − 1500 3000 - P = P - 1500 \Rightarrow 4500 = 2P \Rightarrow P = 2250$$Q = 750 .
Hmm, still not matching. Let me just use the given free market equilibrium:
At free market: P = 1500$$Q = 750 . Demand: Q D = a − b P Q_D = a - bP Q D = a − b P 750 = a − 1500 b 750 = a - 1500b 750 = a − 1500 b Q S = c P − d Q_S = cP - d Q S = c P − d 750 = 1500 c − d 750 = 1500c - d 750 = 1500 c − d
Let me use: Q_D = 2000 - 0.833P$$Q_S = P - 750 . At P = 1500 P = 1500 P = 1500 Q_D = 750.5 \approx 750$$Q_S = 750 . Good enough.
With rent control at P = 1000: Q D = 2000 − 833 = 1167 Q_D = 2000 - 833 = 1167 Q D = 2000 − 833 = 1167 Q S = 1000 − 750 = 250 Q_S = 1000 - 750 = 250 Q S = 1000 − 750 = 250 = 1167 − 250 = 917 = 1167 - 250 = 917 = 1167 − 250 = 917
Black market: Landlords and tenants may illegally trade at above the controlled price. Suppose enforcement is imperfect: probability of detection for illegal renting is 20%, and the fine is GBP 5,000.
Landlord’s expected revenue from black market: If the black market price is P b P_b P b = P b × 0.80 − 5000 × 0.20 = 0.8 P b − 1000 = P_b \times 0.80 - 5000 \times 0.20 = 0.8P_b - 1000 = P b × 0.80 − 5000 × 0.20 = 0.8 P b − 1000
Landlords will participate in the black market if expected revenue exceeds the controlled price: 0.8 P b − 1000 > 1000 ⇒ P b > 2500 0.8P_b - 1000 > 1000 \Rightarrow P_b > 2500 0.8 P b − 1000 > 1000 ⇒ P b > 2500
At P b = 2500 P_b = 2500 P b = 2500 = 1000 = 1000 = 1000
But this assumes the fine is 5000 and detection probability is 20%. If the fine is lower (1000) or detection is less likely (5%):
Expected revenue = P b × 0.95 − 1000 × 0.05 = 0.95 P b − 50 = P_b \times 0.95 - 1000 \times 0.05 = 0.95P_b - 50 = P b × 0.95 − 1000 × 0.05 = 0.95 P b − 50 0.95 P b − 50 > 1000 ⇒ P b > 1105 0.95P_b - 50 > 1000 \Rightarrow P_b > 1105 0.95 P b − 50 > 1000 ⇒ P b > 1105
Now the black market price only needs to exceed 1105 for landlords to participate. The black market would operate at a price between 1105 and 1500 (the free market price).
With weak enforcement: approximately Q S = 750 Q_S = 750 Q S = 750 P b ≈ 1400 P_b \approx 1400 P b ≈ 1400
Key insight: price controls create black markets unless enforcement is extremely rigorous. The resources devoted to enforcement (inspections, legal proceedings) are a deadweight loss. In practice, most economists recommend income support (housing benefit) rather than rent control as a way to help low-income renters without distorting the market.
This topic covers the essential chemistry of demand, supply and equilibrium, including key reactions, underlying theories, and practical applications.
Key concepts include:
dynamic equilibrium and Le Chatelier’s principle the equilibrium constant K c K_c K c K p K_p K p the Haber process acid-base equilibria and pH buffer solutions Mastery of these concepts requires both theoretical understanding and the ability to apply knowledge to unfamiliar contexts, particularly in calculation and practical questions.
Demand and supply is the engine of market economics. The demand curve slopes downward (higher price → less quantity demanded) because of the income and substitution effects. The supply curve slopes upward (higher price → more quantity supplied) because higher prices make production more profitable.
Equilibrium is where the two curves cross — the price at which quantity demanded equals quantity supplied. If the price is too high, there’s a surplus (unsold goods pile up), so sellers lower prices. If too low, there’s a shortage (empty shelves), so sellers raise prices. This natural adjustment is the “invisible hand” that Adam Smith described.
The key distinction for exams is between movements along a curve (caused by price changes) and shifts of the curve (caused by income, tastes, substitutes, complements, etc.). Getting this wrong is the most common error in economics exams. Price controls (ceilings and floors) disrupt this natural adjustment, creating shortages, surpluses, and deadweight loss.
