Question

A firm faces the following linear inverse demand for its product P = 60 - 2Q.
a) Find the firm's total revenue function TR (Q). (4 marks)
b) Find the expression for the firm's marginal revenue. (2 marks)
c) Assuming that the marginal cost of production is given by MC=8. What will be the equilibrium output and price?

Answer 1

a)

$Total \space Revenue=Price\times Quantity$

$TR=P\times Q\\ TR=(60-2Q)Q\\ TR=60Q-2Q^2$

The total revenue function of the firm is :$TR(Q)=60Q-2Q^2$

b) Marginal Revenue:It is the additional revenue obtained by selling an extra output.

Marginal Revenue=Change in Total Revenue$\div$ Change in Output

For this, we will differentiate the Total Revenue(TR) function with respect to output (Q).

$MR=\frac{dTR}{dQ}\\ MR=\frac{d(60Q-2Q^2)}{dQ}\\ MR=60-4Q$

The expression for the firm's marginal revenue is $MR=60-4Q$

 

c) Given: Marginal Cost(MC)=8

At the equilibrium,

Marginal Revenue=Marginal Cost

$MR=MC\\ 60-4Q=8\\ 4Q=60-8\\ 4Q=52\\ Q=\frac{52}{4}\\ Q=13$

The equilibrium output is 13

 Putting value of equilibrium output in the demand function to get the equilibrium price

$P=60-2Q\\ P=60-2(13)\\ P=60-26\\ P=34$

The equilibrium price is 34