FINAL EXAM ANSWER KEY
Version A
I. Multiple choice
(1)c. (2)c. (3)b. (4)d. (5)a. (6)a. (7)b. (8)a. (9)b. (10)c.
(11)d. (12)c. (13)a. (14)c. (15)b. (16)b. (17)a. (18)d.
II. Problems
(1) [Production functions: 12 pts]
- Average product = total output / total input: 3, 4, 5.
- Marginal product = Δ output / Δ input: 3, 5, 7.
- Diminishing returns? NO because MP is increasing.
(2) [Calculating elasticities: 2 pts]
Using arc-elasticity formula:
(ΔQ/Q_{avg}) / (ΔP/P_{avg}) = -1.25 .
(3) [Comparative advantage, gains from trade: 17 pts]
- 2 units of petroleum.
- 4 units of petroleum.
- 1/2 units of wheat.
- 1/4 unit of wheat.
- Country A, because it has lower opportunity cost of producing wheat.
- Country B, because it has lower opportunity cost of producing petroleum.
- Both countries can consume combinations of products outside their individual production possibility curves if Country B exports six units of petroleum to Country B, which exports 2 units of wheat in return.
- Plot should show each country's production before trade, and consumption after trade.
(4) [Market equilibrium: 12 pts]
- excess supply.
- $5.
- 6 units.
- $30 (= price × quantity).
- $57.
- buyers.
(5) [Using income elasticities: 10 pts]
- necessary good.
- increase.
- 3 percent.
- decrease.
- 2 percent.
(6) [Welfare effects of tax or subsidy: 18 pts] Tax = $3: at equilibrium, the demand curve must be higher than the supply curve by $3. Both consumers and producers lose from the tax, but the government gains revenue.
- 8 million gallons.
- $5 per gallon.
- $8 per gallon.
- decrease.
- $9 million.
- decrease.
- $18 million.
- $24 million.
- $3 million.
(7) [Consumer choice and demand: 16 pts]
- 3 smoothies and 4 units of other goods.
- 9 smoothies and 7 units of other goods.
- Budget line A has intercepts at 15 units of other goods and 6 smoothies.
- 4 smoothies.
- Budget line B has intercepts at 15 units of other goods and 10 smoothies.
- 6 smoothies.
- (P,Q) = ($10,4), ($6,6).
(8) [Rational choice: 10 pts]
- MC = Δ TC / Δ miles
= $0.8 million, $0.6 million, $1.0 million, $1.2 million.
- MB = Δ TB / Δ miles
= $4.0 million, $1.2 million, $1.4 million, $0.4 million.
- 1.5 miles, where MB = MC.
(9) [Basic definitions, cost and revenue: 3 pts]
- marginal cost.
- total cost.
- marginal revenue.
(10) [Economy-wide efficiency: 20 pts]
- 3/2 servings French fries.
- 2/3 hamburger.
- $6, because in competitive equilibrium, price equals marginal cost.
- $4, because in competitive equilibrium, prices reflect the slope of the production possibility curve for the economy as a whole: if the opportunity cost of a hamburger is 3/2 servings of French fries, then a hamburger must be 3/2 times as expensive as a serving of French fries.
- $4, because in competitive equilibrium, price equals marginal cost.
- Luke's budget line should have intercept at 30 on French fries axis and intercept of 20 on hamburger axis.
- -3/2, same as slope of country's production possibility curve.
- 3/2 servings of French fries.
- 2/3 hamburgers.
- 3/2, because Luke's preferred bundle is at a tangency between his budget line and the highest indifference curve he can reach, and at a tangency the slope of the indifference curve must equal the slope of the budget line.
(11) [Monopoly, price discrimination: 20 pts] 2 pts for each part, except 1 pt each for parts j and k.
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $14 on price axis, and slope = -1/1 thousand.
- 6 thousand, where MR=MC.
- $11, on demand curve.
- $36 thousand = Rev - TC = (price × quantity) - (AC × quantity).
- $9 thousand.
- $3 thousand.
- 8 thousand, where the demand curve intersects the marginal cost curve, because anyone willing to pay at least the marginal cost will be served.
- $96 thousand, because with every customer paying a different price, revenue = area of the trapezoid under demand curve down to horizontal axis.
- $48 thousand = Rev - TC = Rev - (AC × quantity).
- $0, because consumer surplus is defined as willingness-to-pay minus price, but with perfect price discrimination willingness-to-pay equals price for every customer.
- $0, because with perfect price discrimination, everyone willing to pay the marginal cost is served.
(12) [Regulating pollution: 20 pts]
- Factories A, B, G.
- $700.
- Each factory's willingness-to-pay for a permit equals its annual cost of cleanup. Graph should show downward-sloping stairsteps.
- Factories F, C, D, E.
- $500.
- $700.
- $500.
- $700.
(13) [Externalities: 12 pts]
- $6, at intersection of demand and supply.
- 10 million, at intersection of demand and supply.
- 8 million, at intersection of demand and marginal social cost.
- $6 million, the area of the triangle between marginal social cost, demand, and a vertical line at 10 million liters.
- Tax, to decrease the quantity to the social optimum.
- $5 per liter, which equals the vertical gap between demand and supply and the socially-optimal quantity.
(14) [Nonrival goods: 4 pts]
- MSB = 500 (10-Q) = 5000 - 500 Q.
- 8 movies (found by setting MSB = MC and solving for Q).
(15) [Common property resources: 6 pts]
- 600 cars, where time saved by next car equals zero.
- 300 cars, where change in total time saved by all cars equals zero.
- $3, the dollar equivalent of time saved by next car, at the socially optimal number of cars.
III. Critical thinking [4 pts]
(1) Banning pollution altogether is usually economically inefficient. The optimal amount of a pollution-causing good is where marginal social cost (MSC) equals marginal benefit (MB) or demand. Note that MSC includes the external pollution cost of the good. If output of the pollution-causing good is reduced any further, then the lost MB of each unit of that good to consumers is greater than the avoided MSC, which implies that economic efficiency is reduced.
(2) Given the information in the question, we can calculate that the country's overall welfare increases by $30 million. The graph should show domestic demand and domestic supply intersecting at a price of $10. At a price of $6, quantity demanded is 15 million more than quantity supplied; this difference is imported. The area of the triangle of welfare gain is therefore $30 million. (With the information given, it is not possible to compute separately the gain in consumer surplus or the loss of producer surplus.)
Version B
I. Multiple choice
(1)b. (2)a. (3)d. (4)a. (5)a. (6)c. (7)c. (8)b. (9)c. (10)a.
(11)b. (12)a. (13)c. (14)a. (15)a. (16)d. (17)b. (18)a.
II. Problems
(1) [Production functions: 12 pts]
- Average product = total output / total input: 10, 8, 6.
- Marginal product = Δ output / Δ input: 10, 6, 2.
- Diminishing returns? YES because MP is decreasing.
(2) [Calculating elasticities: 2 pts]
Using arc-elasticity formula:
(ΔQ/Q_{avg}) / (ΔP/P_{avg}) = -1.5 .
(3) [Comparative advantage, gains from trade: 17 pts]
- 1/3 units of petroleum.
- 1 unit of petroleum.
- 3 units of wheat.
- 1 unit of wheat.
- Country A, because it has lower opportunity cost of producing wheat.
- Country B, because it has lower opportunity cost of producing petroleum.
- Both countries can consume combinations of products outside their individual production possibility curves if Country A exports three units of petroleum to Country B, which exports 2 units of wheat in return.
- Plot should show each country's production before trade, and consumption after trade.
(4) [Market equilibrium: 12 pts]
- excess demand.
- $7.
- 5 units.
- $35 (= price × quantity).
- $45.
- sellers.
(5) [Using income elasticities: 10 pts]
- necessary good.
- increase.
- 2 percent.
- decrease.
- 3 percent.
(6) [Welfare effects of tax or subsidy: 18 pts] Subsidy = $3: at equilibrium, the supply curve must be higher than the demand curve by $3. Both consumers and producers gain from the subsidy, but the government must pay.
- 12 million gallons.
- $4 per gallon.
- $7 per gallon.
- increase.
- $11 million.
- increase.
- $22 million.
- $36 million.
- $3 million.
(7) [Consumer choice and demand: 16 pts]
- 4 smoothies and 5 units of other goods.
- 7 smoothies and 5 units of other goods.
- Budget line A has intercepts at 12 units of other goods and 16 smoothies.
- 8 smoothies.
- Budget line B has intercepts at 12 units of other goods and 12 smoothies.
- 7 smoothies.
- (P,Q) = ($3,8), ($4,7).
(8) [Rational choice: 10 pts]
- MC = Δ TC / Δ miles
= $0.6 million, $0.8 million, $1.0 million, $1.2 million.
- MB = Δ TB / Δ miles
= $4.0 million, $0.6 million, $0.6 million, $0.4 million.
- 0.5 miles, where MB = MC.
(9) [Basic definitions, cost and revenue: 3 pts]
- marginal revenue.
- average cost.
- total revenue.
(10) [Economy-wide efficiency: 20 pts]
- 3 servings French fries.
- 1/3 hamburger.
- $6, because in competitive equilibrium, price equals marginal cost.
- $2, because in competitive equilibrium, prices reflect the slope of the production possibility curve for the economy as a whole: if the opportunity cost of a hamburger is 3 servings of French fries, then a hamburger must be 3 times as expensive as a serving of French fries.
- $2, because in competitive equilibrium, price equals marginal cost.
- Luke's budget line should have intercept at 30 on French fries axis and intercept of 10 on hamburger axis.
- -3, same as slope of country's production possibility curve.
- 3 servings of French fries.
- 1/3 hamburgers.
- 3, because Luke's preferred bundle is at a tangency between his budget line and the highest indifference curve he can reach, and at a tangency the slope of the indifference curve must equal the slope of the budget line.
(11) [Monopoly, price discrimination: 20 pts] 2 pts for each part, except 1 pt each for parts j and k.
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $13 on price axis, and slope = -2/1 thousand.
- 4 thousand, where MR=MC.
- $9, on demand curve.
- $24 thousand = Rev - TC = (price × quantity) - (AC × quantity).
- $8 thousand.
- $4 thousand.
- 6 thousand, where the demand curve intersects the marginal cost curve, because anyone willing to pay at least the marginal cost will be served.
- $60 thousand, because with every customer paying a different price, revenue = area of the trapezoid under demand curve down to horizontal axis.
- $36 thousand = Rev - TC = Rev - (AC × quantity).
- $0, because consumer surplus is defined as willingness-to-pay minus price, but with perfect price discrimination willingness-to-pay equals price for every customer.
- $0, because with perfect price discrimination, everyone willing to pay the marginal cost is served.
(12) [Regulating pollution: 20 pts]
- Factories A, B, E, G.
- $1300.
- Each factory's willingness-to-pay for a permit equals its annual cost of cleanup. Graph should show downward-sloping stairsteps.
- Factories F, C, D.
- $700.
- $1300.
- $700.
- $1300.
(13) [Externalities: 12 pts]
- $5, at intersection of demand and supply.
- 8 million, at intersection of demand and supply.
- 12 million, at intersection of marginal social benefit and supply
- $10 million, the area of the triangle between marginal social benefit, supply, and a vertical line at 8 million.
- Subsidy, to increase the quantity to the social optimum.
- $3 per vaccination, which equals the vertical gap between demand and supply and the socially-optimal quantity.
(14) [Nonrival goods: 4 pts]
- MSB = 500 (8-Q) = 4000 - 500 Q.
- 6 movies (found by setting MSB = MC and solving for Q).
(15) [Common property resources: 6 pts]
- 1000 cars, where time saved by next car equals zero.
- 500 cars, where change in total time saved by all cars equals zero.
- $1, the dollar equivalent of time saved by next car, at the socially optimal number of cars.
III. Critical thinking
Same as Version A.
Version C
I. Multiple choice
(1)d. (2)b. (3)c. (4)d. (5)b. (6)d. (7)a. (8)b. (9)d. (10)b.
(11)c. (12)b. (13)b. (14)b. (15)b. (16)a. (17)d. (18)b.
II. Problems
(1) [Production functions: 12 pts]
- Average product = total output / total input: 5, 4, 3.
- Marginal product = Δ output / Δ input: 5, 3, 1.
- Diminishing returns? YES because MP is decreasing.
(2) [Calculating elasticities: 2 pts]
Using arc-elasticity formula:
(ΔQ/Q_{avg}) / (ΔP/P_{avg}) = -2 .
(3) [Comparative advantage, gains from trade: 17 pts]
- 1 units of petroleum.
- 2 units of petroleum.
- 1 units of wheat.
- 1/2 units of wheat.
- Country A, because it has lower opportunity cost of producing wheat.
- Country B, because it has lower opportunity cost of producing petroleum.
- Both countries can consume combinations of products outside their individual production possibility curves if Country B exports two units of petroleum to Country B, which exports 3 units of wheat in return.
- Plot should show each country's production before trade, and consumption after trade.
(4) [Market equilibrium: 12 pts]
- excess supply.
- $9.
- 4 units.
- $36 (= price × quantity).
- $43.
- sellers.
(5) [Using income elasticities: 10 pts]
- luxury (or superior) good.
- increase.
- 6 percent.
- increase.
- 1 percent.
(6) [Welfare effects of tax or subsidy: 18 pts] Subsidy = $6: at equilibrium, the supply curve must be higher than the demand curve by $6. Both consumers and producers gain from the subsidy, but the government must pay.
- 14 million gallons.
- $2 per gallon.
- $8 per gallon.
- increase.
- $24 million.
- increase.
- $48 million.
- $84 million.
- $12 million.
(7) [Consumer choice and demand: 16 pts]
- 4 smoothies and 4 units of other goods.
- 5 smoothies and 5 units of other goods.
- Budget line A has intercepts at 10 units of other goods and 15 smoothies.
- 6 smoothies.
- Budget line B has intercepts at 10 units of other goods and 6 smoothies.
- 3 smoothies.
- (P,Q) = ($2,6), ($5,3).
(8) [Rational choice: 10 pts]
- MC = Δ TC / Δ miles
= $0.6 million, $0.8 million, $1.0 million, $1.2 million.
- MB = Δ TB / Δ miles
= $4.0 million, $1.0 million, $0.4 million, $0.2 million.
- 1.0 miles, where MB = MC.
(9) [Basic definitions, cost and revenue: 3 pts]
- marginal revenue.
- marginal cost.
- marginal cost.
(10) [Economy-wide efficiency: 20 pts]
- 2 servings French fries.
- 1/2 hamburger.
- $6, because in competitive equilibrium, price equals marginal cost.
- $3, because in competitive equilibrium, prices reflect the slope of the production possibility curve for the economy as a whole: if the opportunity cost of a hamburger is 2 servings of French fries, then a hamburger must be 2 times as expensive as a serving of French fries.
- $3, because in competitive equilibrium, price equals marginal cost.
- Luke's budget line should have intercept at 20 on French fries axis and intercept of 10 on hamburger axis.
- -2, same as slope of country's production possibility curve.
- 2 servings of French fries.
- 1/2 hamburgers.
- 2, because Luke's preferred bundle is at a tangency between his budget line and the highest indifference curve he can reach, and at a tangency the slope of the indifference curve must equal the slope of the budget line.
(11) [Monopoly, price discrimination: 20 pts] 2 pts for each part, except 1 pt each for parts j and k.
- Since demand curve is linear, MR curve must have same intercept and twice the slope. So MR curve should have intercept at $14 on price axis, and slope = -1/1 thousand.
- 8 thousand, where MR=MC.
- $10, on demand curve.
- $48 thousand = Rev - TC = (price × quantity) - (AC × quantity).
- $16 thousand.
- $8 thousand.
- 12 thousand, where the demand curve intersects the marginal cost curve, because anyone willing to pay at least the marginal cost will be served.
- $132 thousand, because with every customer paying a different price, revenue = area of the trapezoid under demand curve down to horizontal axis.
- $72 thousand = Rev - TC = Rev - (AC × quantity).
- $0, because consumer surplus is defined as willingness-to-pay minus price, but with perfect price discrimination willingness-to-pay equals price for every customer.
- $0, because with perfect price discrimination, everyone willing to pay the marginal cost is served.
(12) [Regulating pollution: 20 pts]
- Factories A, G.
- $250.
- Each factory's willingness-to-pay for a permit equals its annual cost of cleanup. Graph should show downward-sloping stairsteps.
- Factories B, C, D, E, F.
- $300.
- $250.
- $300.
- $250.
(13) [Externalities: 12 pts]
- $6, at intersection of demand and supply.
- 12 million, at intersection of demand and supply.
- 8 million, at intersection of demand and marginal social cost.
- $8 million, the area of the triangle between marginal social cost, demand, and a vertical line at 8 million liters.
- Tax, to decrease the quantity to the social optimum.
- $3 per liter, which equals the vertical gap between demand and supply and the socially-optimal quantity.
(14) [Nonrival goods: 4 pts]
- MSB = 200 (10-Q) = 2000 - 200 Q.
- 5 movies (found by setting MSB = MC and solving for Q).
(15) [Common property resources: 6 pts]
- 1000 cars, where time saved by next car equals zero.
- 500 cars, where change in total time saved by all cars equals zero.
- $2, the dollar equivalent of time saved by next car, at the socially optimal number of cars.
III. Critical thinking
Same as Version A.
[end of answer key]