Suppose that you are the owner and operator of a perfectly competitive firm with the
following total cost function:
TC = 1,000 + 5Q + 0.02 Q2
Suppose further that the current market price is $25. By definition, TR = P x Q, so your
total revenue function can be stated as:
TR = 25Q

i) Find the profit function (5marks)
ii) Find the optimum quantity (5 marks)
iii) Find the profit

2. (a) Consider a perfectly competitive firm with the following total cost function in the short run:

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STC = 100 + 100Q+ 5Q^2 + (1/3)Q^3

Given the market price of its product is P=$300 per unit, determine its profit-maximizing output and profit for the short run.

(b) Now suppose its long-run total cost is:

LTC= 54Q - 2.4Q^2 + 0.03Q^3

Indicate the firm’s long-run price, quantity sold, and profit, assuming the industry is in long-run equilibrium.

A perfectly competitive firm has a total cost function given by T C(Q) = 2Q3 - 20Q2 + 100Q.

a) What will be the optimal quantity produced by the firm if the market price is P = 300? What will be the profit? (Q=10, Profit=2000)

b) How about if the market price is P = 45? What will be the optimal quantity and profit in this case? (Q=0, Profit=0)

c) Find the break even point and the shut down point. (50)

d) Assuming the initial market price of $300, what will be the optimal quantity and profit if a new fixed cost of $1000 has to be incurred by the firm? How about if this fixed cost is $3000?

A perfectly competitive firm has a total cost function given by T C(Q) = 2Q^3 and 20Q^2 + 100Q.

a) What will be the optimal quantity produced by the firm if the market price is P = 300? What will be the profit? (Q=10, Profit=2000)

b) How about if the market price is P = 45? What will be the optimal quantity and profit in this case? (Q=0, Profit=0)

c) Find the break even point and the shut down point. (50)

d) Assuming the initial market price of $300, what will be the optimal quantity and profit if a new fixed cost of $1000 has to be incurred by the firm? How about if this fixed cost is $3000?