2024 AP AP Microeconomics 模擬試題連答案詳解

(a) Graph Construction (5 points)
- Draw a correctly labeled graph with Price/Cost on the vertical axis and Quantity on the horizontal axis.
- Draw a downward-sloping demand curve (\(D\)) and a downward-sloping marginal revenue curve (\(MR\)) that lies below the demand curve.
- Draw an upward-sloping marginal cost curve (\(MC\)). Identify the profit-maximizing quantity \(Q_1\) where \(MR = MC\) on the horizontal axis.
- Identify the profit-maximizing price \(P_1\) by extending a vertical dashed line from \(Q_1\) up to the demand curve and across to the vertical axis.
- Draw a U-shaped average total cost curve (\(ATC\)) such that \(ATC\) lies below \(P_1\) at \(Q_1\), and \(MC\) passes through the minimum point of \(ATC\).
- Completely shade the triangular area representing deadweight loss (\(DWL\)) bounded by the demand curve on top, the \(MC\) curve on the bottom, between quantity \(Q_1\) and the socially optimal quantity where \(D = MC\).

(b) Fair-Return Regulation (2 points)
- (i) On the graph, label \(Q_R\) on the horizontal axis and \(P_R\) on the vertical axis where the \(ATC\) curve intersects the demand curve (\(P = ATC\)).
- (ii) State that the firm is not producing at allocative efficiency and explain that at \(Q_R\), price is greater than marginal cost (\(P_R > MC\)) or that allocative efficiency occurs where price equals marginal cost (\(P = MC\)).

(c) Elasticity at Profit-Maximizing Output (1 point)
- State that demand is elastic and explain that a single-price monopolist maximizes profit where marginal revenue is positive (\(MR > 0\)), which corresponds strictly to the elastic portion of the demand curve.

(d) Perfect Price Discrimination (2 points)
- (i) State that the total quantity produced will increase and explain that because the firm charges each buyer their maximum willingness to pay, \(MR = D\), and the firm will produce output up to the point where price equals marginal cost (\(P = MC\) / \(D = MC\)), which is greater than \(Q_1\).
- (ii) State that deadweight loss will decrease to zero (or be completely eliminated).

Question 1 Total: 10 points

(a) 5 points:
- 1 point is earned for drawing a correctly labeled graph with a downward-sloping demand (\(D\)) curve and a downward-sloping marginal revenue (\(MR\)) curve below the demand curve.
- 1 point is earned for showing the profit-maximizing quantity \(Q_1\) where \(MR = MC\).
- 1 point is earned for showing the profit-maximizing price \(P_1\) from the demand curve directly above \(Q_1\).
- 1 point is earned for drawing the \(ATC\) curve below \(P_1\) at \(Q_1\) with the \(MC\) curve intersecting the minimum point of \(ATC\).
- 1 point is earned for completely and correctly shading the triangular area of deadweight loss bounded between \(D\) and \(MC\) from \(Q_1\) to the intersection of \(D\) and \(MC\).

(b) 2 points:
- 1 point is earned for identifying and labeling the fair-return price \(P_R\) and quantity \(Q_R\) where \(P = ATC\) (the intersection of \(D\) and \(ATC\)).
- 1 point is earned for stating that the firm is not allocatively efficient AND explaining that price exceeds marginal cost (\(P > MC\)) at \(Q_R\) or that allocative efficiency requires \(P = MC\).

(c) 1 point:
- 1 point is earned for stating that demand is elastic AND explaining that \(MR > 0\) at \(Q_1\) (or total revenue increases as price falls along this region).

(d) 2 points:
- 1 point is earned for stating that total quantity will increase AND explaining that the firm produces output up to where price equals marginal cost (\(P = MC\) or \(D = MC\)).
- 1 point is earned for stating that deadweight loss will decrease to zero (or be eliminated).

(a) $$\text{Average Product of Labor (AP}_L\text{)} = \frac{\text{Total Output}}{\text{Labor}} = \frac{50}{4} = 12.5\text{ panels per worker}$$

(b) $$\text{Marginal Product of 3rd Worker (MP}_3\text{)} = 42 - 30 = 12\text{ panels}$$
$$\text{Marginal Revenue Product (MRP}_3\text{)} = \text{MP}_3 \times P = 12 \times \$5 = \$60$$

(c) The marginal factor cost (MFC) is the market wage rate of $40 per worker.
- MRP of 1st worker: $14 \times $5 = $70 > $40$
- MRP of 2nd worker: $(30 - 14) \times $5 = 16 \times $5 = $80 > $40$
- MRP of 3rd worker: $(42 - 30) \times $5 = 12 \times $5 = $60 > $40$
- MRP of 4th worker: $(50 - 42) \times $5 = 8 \times $5 = $40 = $40$
- MRP of 5th worker: $(55 - 50) \times $5 = 5 \times $5 = $25 < $40$

Apex Cleaners should hire 4 workers because at $L = 4$, $\text{MRP} = \text{MFC} = $40$, and hiring the 5th worker would add less to revenue ($25) than to cost ($40).

(d) At a price of $8 per panel:
- MRP of 4th worker: $8 \times $8 = $64 > $40$
- MRP of 5th worker: $5 \times $8 = $40 = $40$
- MRP of 6th worker: $(57 - 55) \times $8 = 2 \times $8 = $16 < $40$

Therefore, the new profit-maximizing quantity of workers is 5.

(e) Demand for labor will decrease. Because robots and labor are substitutes and the substitution effect dominates the output effect, the decrease in the price of robots leads the firm to employ more capital (robots) and fewer workers at any given wage.

(a) [1 point] for calculating the average product of labor as 12.5 panels per worker and showing the calculation:
$$\frac{50}{4} = 12.5$$

(b) [1 point] for calculating the MRP of the 3rd worker as $60 and showing the calculation:
$$\text{MP} = 42 - 30 = 12$$
$$\text{MRP} = 12 \times \$5 = \$60$$

(c) [1 point] for stating that the profit-maximizing number of workers is 4 and explaining that the MRP of the 4th worker ($40) equals the wage (MFC = $40) and/or hiring the 5th worker would reduce profit because the MRP ($25) is less than the MFC ($40).

(d) [1 point] for identifying the new profit-maximizing number of workers as 5.

(e) [1 point] for stating that demand for labor will decrease and explaining that because robots and labor are substitutes and the substitution effect dominates, the cheaper alternative input will replace labor.

(a) The private market results in overproduction because the unregulated market equilibrium quantity (800 barrels) is greater than the socially optimal quantity (600 barrels).

(b) Deadweight loss is the area between MSC and MSB (which equals MPC/Demand) from the socially optimal quantity to the market equilibrium quantity:
$$\text{DWL} = \frac{1}{2} \times (\text{MSC}_{800} - \text{MSB}_{800}) \times (Q_{\text{market}} - Q_{\text{optimal}})$$
$$\text{DWL} = \frac{1}{2} \times (\$74 - \$50) \times (800 - 600) = \frac{1}{2} \times \$24 \times 200 = \$2,400$$

(c) The government should impose a per-unit corrective (Pigouvian) tax on producers equal to the marginal external cost (MEC) at the socially optimal quantity:
$$\text{MEC} = \text{MSC} - \text{MPC} = \$66 - \$42 = \$24\text{ per barrel}$$

(d) No, the price ceiling will not achieve the socially optimal quantity. A price ceiling of $35 is below the marginal private cost needed to produce 600 units ($42). Because competitive producers supply where $P = \text{MPC}$, at a price of $35, the quantity supplied will be strictly less than 600 barrels, leading to an underproduction relative to the social optimum.

(e) According to the Coase theorem, private parties can reach an efficient solution on their own if:
1. Property rights are well-defined and enforceable.
2. Transaction (bargaining) costs are negligible/zero.

(a) [1 point] for identifying overproduction.

(b) [1 point] for calculating the deadweight loss as $2,400 and showing the work:
$$\frac{1}{2} \times (\$74 - \$50) \times (800 - 600) = \frac{1}{2} \times 24 \times 200 = \$2,400$$

(c) [1 point] for stating that the government should impose a per-unit tax (Pigouvian tax) on producers of $24 per barrel.

(d) [1 point] for stating no and explaining that the price ceiling of $35 will result in a quantity supplied that is less than the socially optimal quantity of 600 barrels (since producing 600 barrels requires a price of at least $42 to cover marginal private cost).

(e) [1 point] for identifying both clearly defined/assigned property rights AND low/negligible transaction (bargaining) costs.