Question

8. Consider a firm producing under conditions of pure competition, in a market characterized by the following demand and supply conditions:

            P = 200 – Qd (Demand);                    P = 100+ Qs (Supply)

a) What is the market equilibrium price and quantity?

b) If a representative firm has a Marginal Cost function that is depicted below, at what level of output would it maximize its individual profits?

MC = 50 + 100q

c) If all of the firms were identical, how many would constitute the market?

Answer 1

8a) At equilibrium,

Demand = Supply.

200 - Q = 100 + Q

2Q = 100

Q = 50 --------> This is the equilibrium quantity of the market.

Setting Q = 50 in the demand function, we have,

P = 200 - Q

P = 200 - 50

P = 150 --------> This is the equilibrium price.

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8b) The optimality condition for a firm is given by,

Price = Marginal Cost

150 = 50 + 100q

100q = 100

q = 1 ---------> This is the equilibrium quantity of a single firm.

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8c) We know that,

Q = n*q, Where Q = Market output, q = Output of a single firm and n = Number of firms in the market.

Thus we have,

50 = n*1

n = 50 -----> This is the number of firms which constitute the market.