Answer to Question #263935 in Macroeconomics for NNNNN

Question

𝑄! =1000−𝑌×𝑝

Assume the marginal cost of the only firm supplying this market as 𝑀𝐶 = 𝑄/2.

a. Derive an expression of elasticity of demand in terms of Y. Show your work.

1. Derive an expression for the slope of the isoprofit curve of this firm in terms of Y. Explain.
2. Now derive an expression for the markup chosen by this firm in terms of Y.
3. What happens to the elasticity (part a) and the markup (part c) if Y goes up? What
4. can you say about the relationship between elasticity and the markup from this
5. observation? Explain.
6. Calculate the profit maximizing quantity and price for the monopolist. What is the
7. maximized profit? Assume fixed cost is 0.

Answer 1

(a)

We are given:

$Q=1000-YP$ and

$MC=\frac{Q}{2}$

Elasticity of demand$=\frac{∆Q}{∆P}\times\frac{P}{Q}$

$E_d=-Y\times\frac{P}{1000-YP}$

$=\frac{YP}{1000-YP}$ .

(1)

Iso profit curve

$Profit=TR-TC$

$TR=\frac{1000Q-Q^2}{r}$

$TC=\frac{Q^2}{4}$

Slope is given as:

$=\frac{4r}{4000-4Q-YQ}$ .

(2)

Expression for Mark up:

$=\frac{4000-4Q^2-Q^2Y}{4r}.$

(3)

If Y goes up, elasticity and mark up will reduce. This is because there exists a negative relationship between them.

(4)

Elasticity and Mark up have a positive relationship. When elasticity is raised Mark up also raises.