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).b)Find the expression for the firm's marginal revenue.c)Assumingthat 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