Question

Suppose the demand for the good was summarized by the equations:

P = 100 – 0.5 Q MR = 100 – Q

and that the marginal cost equals the average costs at $10 per unit.

Calculate the optimum market quantity in a competitive market. (Hint: Set price equal to marginal cost.)

Calculate the quantity brought to market by the monopolist, monopolist’s profit and deadweight loss to society from the monopoly.

Answer 1

Solution : GIVEN :

P= 100 -0.5Q MR =100-Q AND AC = 10

TOTAL COST = 10Q And MC = 10

iF the per unit cost is 10 then total cost is 10Q and and the additional unit cost will be 10.

IN COMPETITIVE MARKET :

P= MC

100-0.5Q = 10

90/0.5 =Q

Therefore Q = 180.

And price = 100- 0.5 * 180 = 100 -90 = 10.

IN CASE OF MONOPOLY :

MR=MC IS THE PROFIT MAXIMIZING POINT SO,

Total reveune = Price * Quantity = (100-0.5Q)*Q = 100Q- 0.5Q^2

Take the partial derivative of TR with respect to Q

You will get MR = 100 - Q

Now equate MR =MC

100-Q = 10

Q= 90.

Price = 100 -0.5 *90 = 100 - 45 =55

Monopoly profit = P*Q -TC = 55 * 90 - 10*90=4950-900 =4050.

Area ABC is the dead weight loss : 1/2 * base * height = 1/2 * (180-90 ) * (55-10) = 2025