Question 2 Suppose that the market demand is described by P= 120-(Q + q) where O

Question

Question 2 Suppose that the market demand is described by P= 120-(Q + q) where O is the output of the incumbent firm. g is the output of the potential entrant and Pis the market price. The incumbent's cost function is given by TC(O) = 600 while the cost function of the entrant is given by TC(Q-60q + 80 (80 is a sunk cost paid upon entering the market) If the entrant observes the incumbent producing Q units of output and expects this level to be maintained, what is the equation for the entrant's demand curve? a. b. If the entrant maximizes profits using the demand in (a). what ouput will the entrant produce? c. How much would the incumbent have to produce to keep the entrant out of the market? At what price will the incumbent sell this output?

Explanation / Answer

a) Entrant Demand Curve : P = 120 - (Q+q)- Q = (120-Q)- q

P = (120-Q)-q

b) Total Revenue = Pq (putting the value of P from point (a))

= ((120-Q)q-q2

Marginal Revenue will be the derviation of TR with respect to q

MR= 120- Q- 2q

Marginal Cost is derivative of TC (MC= 60)

MC= MR

120-Q-2q=60

Solving this equation will give us q = 30- Q/2

c) Profit = (P-c)q-80

Put the value of p and q solve for Q

9

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