Question

Suppose that your total cost of production is TC = 400 + 2Q + .5Q2. You can sell all the output you like at a price of 30 per unit.

a) What is your average total cost?

b) At the current price, what is your optimal level of output?

c) What is your profit at this optimal production level?

Answer 1

Total cost of Production TC= 400 + 2Q +0.5Q²

a) Average total cost is defined as total cost per unit of output. AC= TC/Q

AC = 400/Q + 2 +0.5Q

b) the price of the output is 30 per unit.

Let profit be denoted by P.

The profit is equal to Revenue - Total Cost

Profit (P)= 30Q - 400 - 2Q -0.5Q²

First order condition for Profit maximizing condition is dP/dQ=0 and second order condition is d²p/dQ²<0

dP/dQ= 30 -2 -Q=0 implies Q= 28.

d²P/dQ² = -1<0 Thus second order condition is satisfied.

At the current price, the optimal level of output is Q=28.

c) P= 28Q -400 -0.5Q² = 784 - 400 - 392 = -8