Question

Consider a monopolistically competitive market with N firms. Each firm's business opportunities are described by the following equations:
Demand: Q=100/N-P
Marginal Revenue: MR=100/N-2Q
Total cost: TC=50+Q(squared)
Marginal Cost: MC=2Q

a. How does N, the number of firms in the market, affect each firms demand curve? Why.
b. How many units does each firm produce? (The answer to this and the next two questions depend on N.)
c. What price does each firm charge?
d. How much profit does each firm make?
e. In the long run, how many firms will exist in this market?

Answer 1

(a) Each firm's demand curve is given by the following equation: 100 The demand functionisithal nterceptofthe demand u 100 ; this means that the horizontal intercept of the individual firm declines as the number, N, of firms in the market increases. A fall in horizontal intercept of the demand curve implies a leftward (or inward) shift of the demand curve. (b) To find the number of units that each firm will produce, equate MR and MC. 10020-20 40 100 100 4N 25 Therefore, each firm will produce 25 units of ou

(c) Substitute each firm's production amount in individual firm's demand function. 25 100 100 25 100-25 75 S75 Therefore, each firm will charge a price of dollars (d) Find the total profit that each firm makes by deducting total cost from total revenue. Profit Total Revenue -Total Cost -Pg-(50 + Q2) 75 ( 25 25 50 1875 625 1250 50 1250 Therefore, each firm makes a profit Of| 50

(e) In the long run, firms make zero profit. 1250 72-50-0 1250 25 N°-25 Therefore, only five fims will exist in the long run.

Answer 2

a) With increase in number of firms(N) , the quantity produced decreases as N has inverse relation with Q as seen in the demand equation.

b) For monopolistic competition, each firm produces at a point where ,

MR = MC

100/N - 2Q = 2Q

or, 100/N = 4Q

or, Q* = 25/N

c) We know,

Q = 100/N - P

or, 25/N = 100/N - P

or, 1/N (25-100) = -P

or, 75/N = P*

d) Total Profit = TR - TC = 100Q/N - 4 Q²

= 100(25)/N² - 4(125/N²)

= 2000/N²    

e)

MAXIMIZE Profit = d(TR)dQ - d(TC)/dQ = 0

or,100/N - 4Q - 4Q

or, 100Q/N - 8Q = 0

or, 100Q/N = 8Q

or, N * = 100/8 = 12.5 i.e 12