Version A

I. Multiple choice [2 pt each: 14 pts total]

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

II. Problems

(1) [Marginal revenue: 12 pts]

1. $2.25 .
2. increase.
3. $0.25 .

(2) [Marginal revenue, monopoly pricing, welfare analysis: 24 pts]

1. $11.
2. $4.
3. MR is a straight line with P-intercept at $13 and Q-intercept at 130.
4. 80 devices.
5. $9.
6. $80.

(3) [Monopoly, profit maximization: 28 pts]

1. MC = dTC / dQ = 2 + (Q/200).
2. AC = TC / Q = 2 + (Q/400).
3. TR = P×Q = 17Q - (Q²/200) so MR = dTR / dQ = 17 - (Q/100).
4. Set MR = MC and solve to get Q* = 1000.
5. Substitute Q* into demand equation to get P* = $12.
6. Profit = revenue - TC = (P×Q) - (2Q + Q²400) = $7500.
7. Deadweight loss is the area of a triangle bounded by the demand curve, the marginal cost curve, and a vertical line at the monopoly quantity (1000). Setting demand equal to marginal cost and solving reveals that the two curves intersect at Q=1500. So deadweight loss = 1/2 (12-7) (1500-1000) = $1250.

(4) [Monopoly, markup formula, Lerner index: 8 pts]

1. $2.50 .
2. L = 0.2 .

(5) [Structure-conduct-Performance paradigm: 10 pts]

1. performance.
2. structure.
3. structure.
4. conduct.
5. structure.

III. Critical thinking [5 pts]

On the inelastic part of the demand curve (|ε|<1), MR is negative, because MR = P (1 + (1/ε)). But marginal cost cannot be negative. So MR is always less than MC on this part of the demand curve. Since MR < MC, the firm can increase profit by decreasing output. So a monopolist would never set price and quantity on the inelastic part of its demand curve.

Alternative explanation: When demand is inelastic, then a decrease in output quantity causes price to rise even faster than quantity decreases, and revenue increases. At the same time, a decrease in output quantity always causes total cost to decrease. Since revenue increases and cost decreases, profit increases. Evidently, if the monopolist has chosen price and quantity on the inelastic part of its demand curve, that monopolist has not yet maximized profit.

Version B

I. Multiple choice [2 pt each: 14 pts total]

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

II. Problems

(1) [Marginal revenue: 12 pts]

1. $1.75 .
2. decrease.
3. $0.25 .

(2) [Marginal revenue, monopoly pricing, welfare analysis: 24 pts]

1. $10.
2. $6.
3. MR is a straight line with P-intercept at $13 and Q-intercept at 65.
4. 40 devices.
5. $9.
6. $40.

(3) [Monopoly, profit maximization: 28 pts]

1. MC = dTC / dQ = 1 + (Q/100).
2. AC = TC / Q = 1 + (Q/200).
3. TR = P×Q = 19Q - (Q²/100) so MR = dTR / dQ = 19 - (Q/50).
4. Set MR = MC and solve to get Q* = 600.
5. Substitute Q* into demand equation to get P* = $13.
6. Profit = revenue - TC = (P×Q) - (Q + Q²200) = $5400.
7. Deadweight loss is the area of a triangle bounded by the demand curve, the marginal cost curve, and a vertical line at the monopoly quantity (600). Setting demand equal to marginal cost and solving reveals that the two curves intersect at Q=900. So deadweight loss = 1/2 (13-7) (900-600) = $900.

(4) [Monopoly, markup formula, Lerner index: 8 pts]

1. $8.
2. L = 0.25 .

(5) [Structure-conduct-Performance paradigm: 10 pts]

1. conduct.
2. structure.
3. performance.
4. structure.
5. structure.

III. Critical thinking [4 pts]

(Same as Version A.)

[end of answer key]