Version A

I. Multiple choice [2 pts each: 18 pts total]

(1)c. (2)b. (3)c. (4)c. (5)c. (6)b. (7)a. (8)c. (9)d.

II. Problems

(1) [Transformation of natural monopoly: 25 pts]

1. 9 million.
2. Yes, this is a natural monopoly because cost is subadditive. If 10 million units of output are produced by two firms instead of one firm, total cost will rise.
3. No. (Two firms each producing 9.5 million units of output would have the same average cost as one firm producing 19 million. Put differently, the minimum efficient scale is less than half of total output.)
4. 8 million.
5. Yes. (Two firms each producing 6 million units of output would have higher average cost as one firm producing 12 million. Put differently, the minimum efficient scale is greater than half of total output.)
6. $2.
7. 21 million.
8. 2 firms. (Total output divided by the minimum efficient scale, rounded down because fractional firms are impossible.)

(2) [Multiproduct cost functions: 32 pts]

1. Yes, Tasty Bakery enjoys economies of scope. It is cheaper for one firm to produce two different products, than for two firms to each specialize in a product. For example, C(20,30) < C(20,0) + C(0,30), since 637 < 358 + 329 = 687.
2. IC(Q_P) = $155, $220, $269, $310.
3. AIC(Q_P) = $16, $11, $9, $8.
4. Yes, Tasty Bakery enjoys product-specific economies of scale, because AIC(Q_P) decreases as Q_P increases.

(3) [Cross-subsidization: 20 pts]

1. Yes, the firm is a natural monopoly. If average cost slopes downward, then cost is subadditive. It is cheaper to produce any total output in one firm than in two firms.
2. Market 1: 5 million, Market 2: 10 million.
3. Market 1: loss, Market 2: profit.
4. Market 1: $20 million, Market 2: $20 million (so the firm breaks even).
5. The other firm will enter Market 2 only. The other firm's average cost is less than the regulated price of $8, provided the entrant produces at least 7 million units of output.

III. Critical thinking [5 pts]

Cakes are vulnerable to cream-skimming because cakes are cross-subsidizing pies. Pies are priced below average incremental cost as computed in problem (2c), which implies that cakes are priced above average cost. Here, for example, the average cost of cakes, when 30 cakes are produced, is AC_C(30) = $14.60, which is less than the regulated price of $20 for cakes. So an entrant producing only cakes would be profitable. (Pies are not vulnerable to cream-skimming because the average cost of pies is greater than the regulated price of $4 for pies at all levels of output.)

Version B

I. Multiple choice [2 pts each: 18 pts total]

(1)b. (2)a. (3)d. (4)a. (5)d. (6)a. (7)c. (8)b. (9)d.

II. Problems

(1) [Transformation of natural monopoly: 25 pts]

1. 11 million.
2. Yes, this is a natural monopoly because cost is subadditive. If 13 million units of output are produced by two firms instead of one firm, total cost will rise.
3. Yes. (Two firms each producing 8 million units of output would have higher average cost than one firm producing 16 million. Put differently, the minimum efficient scale is greater than half of total output.)
4. 5 million.
5. No. (Two firms each producing 7.5 million units of output would have the same average cost as one firm producing 15 million. Put differently, the minimum efficient scale is less than half of total output.)
6. $3.
7. 18 million.
8. 3 firms. (Total output divided by the minimum efficient scale, rounded down because fractional firms are impossible.)

(2) [Multiproduct cost functions: 32 pts]

1. Yes, Tasty Bakery enjoys economies of scope. It is cheaper for one firm to produce two different products, than for two firms to each specialize in a product. For example, C(40,30) < C(40,0) + C(0,30), since 905 < 641 + 333 = 974.
2. IC(Q_P) = $77, $220, $392, $584.
3. AIC(Q_P) = $8, $11, $13, $15.
4. No, Tasty Bakery does not enjoy product-specific economies of scale, because AIC(Q_P) increases as Q_P increases.

(3) [Cross-subsidization: 20 pts]

1. Yes, the firm is a natural monopoly. If average cost slopes downward, then cost is subadditive. It is cheaper to produce any total output in one firm than in two firms.
2. Market 1: 15 million, Market 2: 6 million.
3. Market 1: profit, Market 2: loss.
4. Market 1: $15 million, Market 2: $15 million (so the firm breaks even).
5. The other firm will enter Market 1 only. The other firm's average cost is less than the regulated price of $5, provided the entrant produces at least 11 million units of output.

III. Critical thinking [5 pts]

Pies are vulnerable to cream-skimming because pies are cross-subsidizing cakes. Cakes are priced below average incremental cost as computed in problem (2c), which implies that pies are priced above average cost. Here, for example, the average cost of pies, when 20 pies are produced, is AC_P(20) = $9.85, which is less than the regulated price of $16 for pies. So an entrant producing only pies would be profitable. (Cakes are not vulnerable to cream-skimming because the average cost of cakes is greater than the regulated price of $5 for cakes at all levels of output.)

[end of answer key]