Question

The Zenith television company faces a demand function for its products which can be expressed as Q = 4000 – P + 0.5Y where Q is the number of televisions, P is the price per television, and Y is average monthly income. Average monthly income is currently equal to RM2,000.

 

a) Express the inverse demand curve faced by Zenith at the current income level. (2 marks)

 

b) At what price and quantity is Zenith’s total revenue (TR) maximum? State the maximum TR value. Show the value of marginal revenue at this price and quantity. (4 marks)

 

c) What is the price elasticity of demand for Zenith’s demand function at the price and quantity derived in (b)? Interpret. (3 marks)

 

d) Why might Zenith choose to produce at a price and quantity different than that derived in (b)? (3 marks)

Answer 1

Part a

$Q=4000-P+0.5Y$

$Q=4000-P+0.5*2000$

$Q=4000-P+1000$

$Q=5000-P$

$P=5000-Q$

Part b

$TR = PQ$

$(5000-Q)Q=5000Q-Q^2$

To maximize TR put $\frac{\partial TR}{\partial Q}=0$

$\frac{\partial TR}{\partial Q}=5000-2Q=0 \implies Q= 2500$

$P=5000-2500=2500 \implies TR=PQ =2500*2500=6250000$

$MR =5000-2Q \implies MR =0$

Part c

Price elasticity $= \frac{dTR}{dP}* \frac{P}{Q}$

$\implies -1 (\frac{2500}{2500})=-1$

With 1 percent increase on the price, the quantity demanded decreases by 1 percent.

Part d

It is not necessary for Zenith to choose the $Q=2500+ p=2500$ because here there is only total revenue maximization Zerith would want the profit maximization but here cost is not given.