Consider a market comprised of three firms. Firm 1 produces and sells 23 units p

Question

Consider a market comprised of three firms. Firm 1 produces and sells 23 units per period. Firm produces and sells 19 units per period, while firm 3's periodic production and sales are 15 units. The (inverse) market demand is estimated to be: P = 100 - Q, where Q = total output = q_1 + q_2 + q_3. Determine the market price and the elasticity of market demand as well as the market share of each firm. Now use equation (3.5) to determine each firm's marginal cost. What relation do you find between marginal cost and market share

Explanation / Answer

If P = 100 - Q, then Q = 100 - P

Q = q1 q2 + q3

Q = 23 + 19 + 15 = 57

P = 100 - Q = 100 - 57 = 43

Elasticity of demand = (dQ/dP) x (P/Q) = - 1 x (43/57) = - 0.75

Market share, firm 1 = 23/57 = 0.4035, or 40.35%

Market share, firm 2 = 19/57 = 0.3333, or 33.33%

Market share, firm 1 = 15/57 = 0.2632, or 26.32%

NOTE: Marginal cost equation is not given, so MC can't be computed.

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