Question

demand p=20-q

total cost =20+q+q^2

find

price ,quantity, and profit for a monoplist firm

price ,quntitiy, and profit for purely commpetitive firm

Answer 1

a)

In case of monopolist firm

Demand is given by

p=20-q

Total Revenue=p*q=(20-q)*q=20q-q²

Marginal Revenue=MR=dTR/dq=20-2q

Total Cost is given by

TC=20+q+q²

Marginal Cost=MC=dTC/dq=1+2q

Set MR=MC for profit maximization

20-2q=1+2q

19=4q

q=4.75

p=20-q=20-4.75=15.25

Total Revenue=TR=p*q=15.25*4.75=72.4375

Total Cost=TC=20+q+q²=20+4.75+4.75²=47.3125

Profit=TR-TC=72.4375-47.3125=25.125

In case of monopolist

Price=15.25

Output=4.75

Profit=25.125

b)

In case of perfect competitive firm

Demand is given by

p=20-q

Total Revenue=p*q=(20-q)*q=20q-q²

Total Cost is given by

TC=20+q+q²

Marginal Cost=MC=dTC/dq=1+2q

Set MC=P for profit maximization

1+2q=20-q

3q=19

q=6.33333

p=20-q=20-6.33333=13.66667

Total Revenue=p*q=13.66667*6.33333=86.5555

Total Cost=TC=20+q+q²=20+6.33333+6.33333²=66.4444

Profit=TR-TC=86.5555-66.4444=20.1111

In case of perfect competitive firm

Price=13.66667

Output=6.33333

Profit=20.1111