# solution

In Lectures 20 and 21 we worked through an algebraic model of monopolistic competition. Use your notes to answer the following questions.

Throughout, set marginal cost c and fixed cost f equal to 1.

(Instruction) For questions 1 and 2, assume there are N = 9 firms in the industry in autarky. The population is L= 144.

Question 1

If a single firm reduces price by 0.1, its sales (output) will increase by _______ if no other firm changes price.

Question 2

If all firms reduce price by 0.1 at the same time, sales (output) of each firm will increase by _______.

(Instruction) For the remaining questions, assume there are two identical countries. Each country has a population of L = 144.

Question 3

For each country, the autarky equilibrium number of firms is _______.

Question 4

For each country, the autarky equilibrium price is _______ (round to three decimal places).

Question 5

For each country, the autarky equilibrium output per firm is _______.

Question 6

For each country, the autarky equilibrium average cost per firm is _______ (round to three decimal places).

Question 7

For each country, the autarky equilibrium price-cost margin per firm is _______ (round to three decimal places). Hint: price-cost margin is defined as the difference between price and marginal cost.

(Instruction) Now suppose the two countries can trade costlessly with each other. Answer the following questions for the free-trade equilibrium.

Question 8

The total number of firms is _______ (round to the nearest integer).

Question 9

The equilibrium price is _______ (round to three decimal places).

Question 10

The equilibrium output per firm is _______ (round to three decimal places).

Question 11

The equilibrium average cost per firm is _______ (round to three decimal places).

Question 12

The equilibrium price-cost margin per firm is _______ (round to three decimal places).

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