Question

PART I: Consider a market with the following demand: P(Q) = 20 - Q Assume that the market is served by a single firm, Firm Wire, with the following cost: C(Q) = Q2 + 3Q + 10 1- Write the profit expression of Firm Wire. 2- Find the output choice of Firm Wire. 3- How much does the monopolist charge? 4 . + der Wirin.2

Answer 1

P = 20 - Q

TC = Q²+3Q+10

As there is a single firm so it is a monopolist

Profit = Total Revenue(TR) - Total Cost(TC)

Total Revenue= P*Q

TR= 20Q - Q²

Profit = 20Q - Q² - Q² - 3Q - 10

Profit = -2Q² + 17Q -10

This is the profit fucnction

For calculating output choice we must note that monopolist produce at that point where MR=MC

So MR = 20 - 2Q

MC = 2Q+3

MR = MC

20 - 2Q = 2Q + 3

4Q = 17

Q= 4.25

Thus monopolist will produce 4.5 units of output

Price charged will be

P = 20 - 4.25 = 15.75

Profit earned = P*Q - TC = 15.75* 4.25 - (4.25)² - 3(4.25) - 10

Profit = 66.9375 - 18.0625 - 12.75 - 10

Profit = 26.125

Thus monopolist will earn 26.125