Question

22. Consider a monopolistically competitive market. Despite producing differentiated products, suppose that each existing firm (and any potential entrant) has the same total cost function, given by TC=2200+100Q+Q². And despite producing differentiated products, suppose that each existing firm currently faces the same residual demand curve, given by Q=(320-P)/4.5 What will happen in the market over the long run?

      A. Number of firms will increase and residual demand of existing firms will shift leftward.

      B. Number of firms will decrease and residual demand of remaining firms will shift rightward.

      C. Number of firms will stay the same and residual demand of existing firms will not change.

      D. Number of firms will increase and residual demand of existing firms will shift rightward.

      E.   Number of firms will decrease and residual demand of remaining firms will shift leftward.

Answer 1

For each firm in the given monopolistic competition:

TC = 2200 + 100Q + Q^2

Marginal Cost, MC = d/dQ (TC) = d/dQ (2200 + 100Q + Q^2) = 0 + 100 * 1 + 2Q = 100 + 2Q

Q = (320-P)/4.5 => 4.5Q = 320 - P => P = 320 - 4.5Q

Total Revenue, TR = Price * Quantity = (320 - 4.5Q) * Q = 320Q - 4.5Q^2

Marginal Revenue, MR = d/dQ (TR) = d/dQ (320Q - 4.5Q^2) = 320 - 4.5*2Q = 320 - 9Q

At the profit-maximizing level of output, MC = MR

=> 100 + 2Q = 320 - 9Q

=> 2Q + 9Q = 320 - 100

=> 11Q = 220

=> Q = 220/11 = 20

The profit-maximizing quantity of output = 20 units

When Q = 20, TC = 2200 + 100*20 + 20^2 = 2200 + 2000 + 400 = $4600

TR = 320*20 - 4.5*20^2 = $4600

Profit = TR - TC = $4600 - $4600 = 0

As all the firms in the given monopolistically competitive market are earning zero economic profit, all the firms continue to produce in the long run and no entry or exit of firms would take place.

Ans:  C. Number of firms will stay the same and residual demand of existing firms will not change.