2023 AP AP Microeconomics 模擬試題連答案詳解

### Part (a)
AuraClean continues to operate in the short run because the market price (\(P\)) is greater than or equal to its average variable cost (\(AVC\)) at the profit-maximizing output level (or total revenue covers total variable cost, \(TR \ge TVC\)). By continuing to produce, the firm generates enough revenue to cover all variable costs and contribute toward covering fixed costs, resulting in a smaller loss than if it were to shut down and lose all fixed costs.

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### Part (b)
- Market Graph:
- Vertical axis labeled Price (or \(P\)), horizontal axis labeled Quantity (or \(Q\)).
- Downward-sloping market demand curve (\(D\)) and upward-sloping market supply curve (\(S\)).
- Equilibrium price labeled \(P_M\) and equilibrium quantity labeled \(Q_M\) at the intersection of \(D\) and \(S\).
- Firm Graph (AuraClean):
- Vertical axis labeled Price / Cost, horizontal axis labeled Quantity (or \(q\)).
- Perfectly elastic horizontal demand and marginal revenue curve: \(d = \text{MR}\), extended horizontally from the market equilibrium price \(P_M\), labeled \(P_F\).
- Upward-sloping marginal cost curve (\(MC\)).
- Output \(Q_F\) determined where \(\text{MR} = \text{MC}\).
- Average total cost (\(ATC\)) curve drawn U-shaped, lying above \(P_F\) at \(Q_F\), with \(MC\) passing through the minimum point of \(ATC\).
- Average variable cost (\(AVC\)) curve drawn U-shaped, lying below \(P_F\) at \(Q_F\), with \(MC\) passing through the minimum point of \(AVC\).
- Economic loss is the rectangle between \(P_F\) and \(ATC\) at quantity \(Q_F\), shaded completely.

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### Part (c)
- Market Graph Adjustment:
- Because firms are incurring short-run economic losses, firms will exit the industry in the long run.
- The market supply curve shifts to the left from \(S\) to \(S_2\).
- This shift results in a higher market equilibrium price labeled \(P_2\) and a lower market equilibrium quantity labeled \(Q_2\).
- Firm Graph Adjustment:
- AuraClean faces a higher price \(P^* = P_2\), which corresponds to the minimum point on its \(ATC\) curve.
- The new profit-maximizing output is labeled \(Q^*\), where \(P^* = \text{MR}_2 = MC = \text{minimum } ATC\), yielding zero economic profit.

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### Part (d)
(i) Marginal Revenue Product of labor (\(\text{MRP}_L\)) is calculated as:
\[ \text{MRP}_L = \text{Marginal Product} \times \text{Price of Output} \]
\[ \text{MRP}_L = 50 \times \$4 = \$200 \]

(ii) AuraClean should hire more workers.
Explanation: A profit-maximizing firm in a competitive labor market hires workers up to the point where \(\text{MRP}_L = \text{MFC}\) (where \(\text{MFC} = \text{Wage}\)). Since the marginal revenue product of the last worker hired (\(\$200\)) exceeds the marginal factor cost / wage (\(\$160\)), hiring additional workers adds more to total revenue than to total cost, thereby increasing total profit.

Question 1 Breakdown (10 points total):

- Part (a): 1 point
- 1 point for explaining that the market price is greater than average variable cost (\(P > AVC\)) or that total revenue is greater than total variable cost (\(TR > TVC\)), allowing the firm to cover its variable costs and minimize losses.

- Part (b): 4 points
- 1 point for drawing a correctly labeled market graph with downward-sloping demand (\(D\)), upward-sloping supply (\(S\)), and labeling the market equilibrium price as \(P_M\) and quantity as \(Q_M\).
- 1 point for drawing a correctly labeled firm graph with a horizontal demand and marginal revenue (\(d = \text{MR}\)) curve extended from \(P_M\) and labeling the firm's price as \(P_F\).
- 1 point for showing an upward-sloping marginal cost (\(MC\)) curve and labeling the profit-maximizing output \(Q_F\) where \(\text{MR} = \text{MC}\).
- 1 point for drawing the \(ATC\) curve above \(P_F\) at \(Q_F\), \(AVC\) curve below \(P_F\) at \(Q_F\), with \(MC\) passing through the minimum of \(ATC\) and \(AVC\), and completely shading the rectangular area of economic loss.

- Part (c): 2 points
- 1 point for showing a leftward shift of the market supply curve (\(S_2\)), resulting in a higher market equilibrium price labeled \(P_2\) and a lower market equilibrium quantity labeled \(Q_2\).
- 1 point for showing the firm's higher price \(P^*\) extended from \(P_2\) and labeling the new profit-maximizing quantity \(Q^*\) at the minimum of the \(ATC\) curve where \(P^* = \text{MR}_2 = MC = \text{min } ATC\).

- Part (d): 3 points
- 1 point for correctly calculating \(\text{MRP} = \$200\) and showing the work: \(\text{MRP} = \text{MP} \times P = 50 \times \$4 = \$200\).
- 1 point for stating that AuraClean should hire more workers.
- 1 point for explaining using marginal analysis that the marginal revenue product (\(\$200\)) is greater than the marginal factor cost / wage (\(\$160\)).

(a) Marginal product of the 2nd worker: \(\text{MP}_2 = 19 - 8 = 11\text{ units}\).
\(\text{MRP}_2 = \text{MP}_2 \times P = 11 \times \$4 = \$44\).

(b) Marginal product for each worker:
- Worker 1: \(8 - 0 = 8\)
- Worker 2: \(19 - 8 = 11\)
- Worker 3: \(27 - 19 = 8\)
- Worker 4: \(33 - 27 = 6\)
- Worker 5: \(36 - 33 = 3\)
- Worker 6: \(37 - 36 = 1\)
Marginal product increases from worker 1 to worker 2 (from 8 to 11) and begins to decrease with worker 3 (from 11 to 8). Therefore, diminishing marginal returns begin with the hiring of the 3rd worker.

(c) \(\text{MRP} = \text{MP} \times \$4\):
- 1st worker: \(8 \times \$4 = \$32 > \$20\)
- 2nd worker: \(11 \times \$4 = \$44 > \$20\)
- 3rd worker: \(8 \times \$4 = \$32 > \$20\)
- 4th worker: \(6 \times \$4 = \$24 > \$20\)
- 5th worker: \(3 \times \$4 = \$12 < \$20\)
The profit-maximizing number of workers is 4. The firm hires the 4th worker because \(\text{MRP}_4 (\$24) > \text{MFC} (\$20)\), but will not hire the 5th worker because \(\text{MRP}_5 (\$12) < \text{MFC} (\$20)\).

(d) At 4 workers:
\(\text{Total Revenue (TR)} = P \times Q = \$4 \times 33 = \$132\).
\(\text{Total Cost (TC)} = \text{TFC} + \text{TVC} = \$30 + (4 \times \$20) = \$30 + \$80 = \$110\).
\(\text{Economic Profit} = \text{TR} - \text{TC} = \$132 - \$110 = \$22\).

(e) The profit-maximizing number of workers will decrease (from 4 to 3 workers). At a wage of $28, \(\text{MFC} = \$28\). The MRP of the 4th worker is $24, which is now less than the marginal factor cost ($28), meaning the 4th worker would add more to cost than to revenue.

(a) [1 mark]: State $44 and show the calculation: \(\text{MRP} = \text{MP} \times P = (19 - 8) \times \$4 = 11 \times \$4 = \$44\).
(b) [1 mark]: State that diminishing marginal returns begin with the hiring of the 3rd worker.
(c) [1 mark]: State that the profit-maximizing number of workers is 4 and explain that the MRP of the 4th worker ($24) is greater than the MFC/wage ($20), while the MRP of the 5th worker ($12) is less than the MFC/wage ($20).
(d) [1 mark]: Calculate economic profit as $22 and show valid work: \(\text{Profit} = (\$4 \times 33) - [\$30 + (4 \times \$20)] = \$132 - \$110 = \$22\).
(e) [1 mark]: State that the number of workers hired will decrease and explain that the new wage/MFC ($28) exceeds the MRP of the 4th worker ($24).

(a) Yes, Brewed Awakening has a dominant strategy to choose the Loyalty Discount.
- If Daily Grind chooses Loyalty Discount, Brewed Awakening earns $400 with Loyalty Discount versus $200 with Regular Pricing ($400 > $200).
- If Daily Grind chooses Regular Pricing, Brewed Awakening earns $700 with Loyalty Discount versus $600 with Regular Pricing ($700 > $600).
Since Loyalty Discount yields higher profits regardless of Daily Grind's choice, it is a dominant strategy.

(b) Daily Grind faces the exact symmetric payoffs, so Daily Grind's dominant strategy is also Loyalty Discount ($400 > $200 and $700 > $600). The Nash equilibrium is for both firms to choose (Loyalty Discount, Loyalty Discount), resulting in payoffs of ($400, $400).

(c) Combined profits for each outcome:
- (Loyalty, Loyalty): \(\$400 + \$400 = \$800\)
- (Loyalty, Regular): \(\$700 + \$200 = \$900\)
- (Regular, Loyalty): \(\$200 + \$700 = \$900\)
- (Regular, Regular): \(\$600 + \$600 = \$1,200\)
To maximize combined profits, both firms will choose Regular Pricing.

(d) No, the Nash equilibrium will not change. A lump-sum tax is a fixed cost that reduces every payoff by exactly $150. It does not affect marginal benefits or costs of either strategy, so the payoff ranking remains identical (e.g., \(\$250 > \$50\) and \(\$550 > \$450\)).

(e) Daily Grind's dominant strategy remains Loyalty Discount. With the $150 subsidy added to Loyalty Discount payoffs:
- If Brewed Awakening chooses Loyalty Discount, Daily Grind earns \(\$400 + \$150 = \$550\) from Loyalty Discount versus $200 from Regular Pricing (\(\$550 > \$200\)).
- If Brewed Awakening chooses Regular Pricing, Daily Grind earns \(\$700 + \$150 = \$850\) from Loyalty Discount versus $600 from Regular Pricing (\(\$850 > \$600\)).
Since Loyalty Discount is strictly better in both cases, Loyalty Discount is Daily Grind's dominant strategy.

(a) [1 mark]: State yes, Loyalty Discount, and explain using values from the matrix showing that Brewed Awakening earns higher profits with Loyalty Discount regardless of Daily Grind's action ($400 > $200 and $700 > $600).
(b) [1 mark]: Identify the Nash equilibrium as (Loyalty Discount, Loyalty Discount) or both choosing Loyalty Discount.
(c) [1 mark]: State that both firms will choose Regular Pricing (or Brewed Awakening: Regular Pricing, Daily Grind: Regular Pricing).
(d) [1 mark]: State no, and explain that a lump-sum tax reduces all payoffs equally by $150 and does not change marginal payoffs or relative choices.
(e) [1 mark]: State that Daily Grind has a dominant strategy of Loyalty Discount and support the answer using updated payoff comparisons ($550 > $200 and $850 > $600).