Answer to Question #130414 in Microeconomics for Amanuel

Question

A firm faces the demand function p = 190 − 0.6q and the total cost function TC = 40 + 30q + 0.4q2 
(a) What output will maximize profit? 
(b) What output will maximize total revenue? 
(c) What will the output be if the firm makes a profit of 4,760?

Answer 1

a)

$$MC=p$$

$$MC=30+0.8q$$

$$30+0.8q=190-0.6q$$

$$q=114$$

b)

$$TR=pq$$

$$TR=190q-0.6q^2$$

$$TR^/=190-1.2q$$

$$q=158$$

c)

$$TR-TC=160q-q^2-40$$

$$160q-q^2-40=4760$$

$$q=185$$