Answer to Question #253580 in Macroeconomics for ROBOT

Question

Consider a market with the following demand curve:

𝑄^d=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

B.Derive an expression for the slope of the isoprofit curve of this firm in terms of Y. Explain.

c.Now derive an expression for the markup chosen by this firm in terms of Y.

d.What happens to the elasticity (part a) and the markup (part c) if Y goes up? What can you say about the relationship between elasticity and the markup from this observation? Explain.

e.calculate the profit-maximizing quantity and price for the monopolist. What is the maximized profit? Assume fixed cost is 0.

Answer 1

Given

$Q=100-YP\\MC=\frac{Q}{2}$

a)

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

Hence $Q=100-YP$

$Ed=-Y×\frac{P}{1000-YP}\\ Ed=\frac{-YP}{1000-YP}$

b.

isoprofit curve

$Profit=TR-TC\\TR=\frac{1000Q-Q^2}{r}\\TC=\frac{Q^2}{4}$

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

c.

Mark up

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

d.

Elasticity and markup will reduce when Y goes up.This is because they have a negative relationship. Elasticity and markup have a positive relationship.