Consider the demand function:

Q=-5p² -7.5p+800

where q = quantity, p = price

a)

Find Total Revenue as a function of p

(Hint: Do not attempt to find Total Revenue as a function of q, as to do so quires use of the inverse demand function which is difficult to find in this case.

(2 marks)

b) Show that when-15p-15p+800=0, Total Revenue is at its

maximum.

Find the price and quantity that maximise Total Revenue.

(3 marks)

c) Show that the demand elasticity, as a function of p, is given

by:

A

+

E=(-10p-7.5p)/(-5p'-7.5p+800)

Show that when demand has unit elasticity (that is, E*=-1 or |E^d| = 1), Total

Revenue is at its maximum.

(4 marks)

d)

For what values of p is demand (i) elastic; (ii) inelastic? What is the effect of a small price reduction on Total Revenue, when demand is (i) elastic; (ii) inelastic?

[4 marks)

e)

Sketch the graphs of the Demand function, Total Revenue and Marginal Revenue as functions of p.

(3 marks)

Explain, using words and diagrams only, the relationship

between Marginal Revenue and the Elasticity of Demand.

(4 marks))​