Question

Economics 433: Advanced International Trade

SP 2018

Homework 7: Due in Class, March 20

Problem (Monopolistic Competition)

A firm located in Home is making a variety of a differentiated good in a monopolistically competitive industry. The firm needs 20 workers to maintain its plant (fixed cost) and one worker per unit of output (marginal cost). Each worker costs $5.

a. In autarky, the firm sells 10 units and is breaking even. What price is it charging?

b. Home goes from autarky to free trade. In the new long-run equilibrium, the firm charges $10 per car. How has the firm’s productivity (output per worker) changed?

c. Explain, using the appropriate diagram, how trade caused the output and price charged by the firm to change.

Answer 1

Answer:-

Fixed cost, FC = 20 workers x $5 per worker = $100

Variable cost, VC = 5Q [Since number of workers per unit = 1]

Total cost, TC = FC + VC = 100 + 5Q

(B)

Q = 10

In break-even, revenue = TC

P x Q = 100 + 5Q

P x 10 = 100 + 50 = 150

P = 150 / 10 = 15

Price is $15.

(B)

New price = $10

TC = 100 + 5Q

New revenue = $10 x Q

Equating,

100 + 5Q = 10Q

5Q = 100

Q = 20

Earlier, 1 worker was required to produce 1 unit of output. So, to produce 10 units, 10 workers were required.

Now, 10 workers can produce 20 units (Since question doesn't mention additional of workers or change in variable cost).

Hence, productivity has doubled.

(B)

Initial (Price, output) = ($15, 10)

Changed (Price, Output) = ($10, 20)

As productivity ahs doubled, the firm has increased its supply, shifting supply curve from S0 to S1. Price has decreased from $15 to $10 and output increased from 10 to 20 units.