Q1. A price searching firm faces the following demand and cost function:
P = 100 - Q
TC = 10Q + 10
a) What is the optimal price and quantity for this firm? To do this, first establish the firm's MR and MC curves and then graph them (and the demand curve) on graph paper.
b) What is the firm's profit or loss?
c) What is the level of output and price if it were a perfectly competitive market? Show and explain this result.
Q2. Suppose a market can be separated into two distinct market segments, where:
P1 = 42 - 4Q1
P2 =22 - 2Q2
TC = 5 + 10(Q1 + Q2)
a) What is the firm's marginal cost and marginal revenue? For the marginal cost, it might help to make a cost table and examine how TC changes if Q1 or Q2 is increased.
b) Graph the two market segments' demand curve, MR, and MC.
c) What is the profit maximizing level of output and the price per unit in each segment of the market?
d) Calculate the elasticity of demand at these profit maximizing prices. Comment.