Question

Competition & Monopoly Problems.

1. Competition: Assume: Qd = 625 -5p Qs = 175 +5P TC = 1 + 5Q + 4Q2 Find: Profit max P, Q, TR, TC, profit.

2. Monopoly: Assume: P = 45 - .5Q TC = 3Q2 + 15Q -12 Find: Profit max P, Q, TR, TC, profit and elasticity.

Answer 1

1. Under perfect competition equilibrium is attained at the intersection of the demand and supply curve. At equilibrium quantity demand (Qd) = quantity supplied (Qs).

At Qd=Qs

625-5p=175+5p

P=45

Q=400.

TR=P×Q (price × quantity)=45×400= 18000

TC= 1+ 5Q + 4Q^2 = 642001

Profit = TR-TC = 18000-642001= -624001

Thus the firm's are making losses.

2. Monopolist maximize their profits by equating marginal revenue to marginal cost. Here marginal revenue is obtained by differentiating the total revenue Function with respect to quantity.

The profit function of the monopolist is given by:

Profit= price×quantity - total cost

π = P×Q - TC

π = (45 - 0.5Q)×Q - 3Q^2-15Q +12

Differentiating with respect to quantity and equating the equation to zero. (First order condition) we get:

45 - Q - 6Q -15= 0

7Q=30

Q=30/7

P = 45 - 0.5Q = 45 - 15/7 = 300/7

TR = P×Q = 300/7 × 30/7 = 9000/49

TC = 3Q^2 + 15Q - 12 = 5262/49

Profits : π = TR - TC = (9000-5262)/49 = 3738/7 = 534

Elasticity : e=( dQ/dP)×P/Q

dQ/dP = -2 ( differentiating the demand equation with Q)

e= -2×(300/7×7/30)= -20.