Question

1- Given a Perfect competition firm cost function

C(Q) = 5 + Q2        &    Market Price (P = $10 )

-     Find MR

-     Maximum Profits p?

-     What is the Effect of Entry on Firms Output & Profit ?

2- If You are a monopolist with an inverse demand

P = 100 – Q

and Cost Function        C(Q) = 125+4Q2

-     Find Q* and P*

-     Max Tp

Answer 1

1)

C (Q) = 5 + Q^²

Market price = $10

• Marginal revenue is the price producer receive from selling additional unit.
• Marginal cost (first derivative of total cost with respect to Q) = 2Q

Profit occurs when marginal revenue = marginal cost

2Q = 10

Q = 5

At Q = 5, total cost = 5 + 5 ^² = 30 while total revenue is 10 * 5 = 50 which means there will be prfit of 50 - 30 = 20

• As firm is making positive profit in short run, many new firms will join the market in long run by obsering profit in short run. It will divide profit in all firms and reduce it to such an extent that they only earn normal profit in long run.

2) P = 100 - Q

C (Q) = 125 + 4Q^²

Monopolist operate when MR = MC

TR = P * Q = 100Q - Q^²

MR (first derivative of TR with respect to Q) = 100 - 2Q

MC (first derivative of TR with respect to Q) = 8Q

Profit maximizing point: MR = MC

100 - 2Q = 8Q

Q = 10

At this Q, P = 90

• At this Q, TC = 125 + 4 * 10^²= 525 while TR = 100 * 10 - 10^² = 900 which result in profit of 900 - 525 = 375