Question 4 (15 marks)
Suppose you work for a firm that produces good x. Demand for this good depends on
the food's own price, the prices of related goods y and z, and consumer income.
$Q_x^d=100-3P_x-1.5P_y+2P_z+0.01I$
where
$P_x=$20
$P_y=$10
$P_z=$50
$I=$60,000
Page 4 of 4
1) What is the own price elasticity of demand for good x? (1 mark)
2) What is the cross-price elasticity of demand for goods x and y? (1 mark)
3) What is the cross price elasticity of demand for goods x and z? (1 mark)
4) What is the income elasticity of demand for good x? (1 mark)
5) Is demand for good x elastic or inelastic, with respect to its own price? Why?
(1 mark)
6) Is good x a normal or an inferior good? Why? (1 mark)
7) Are goods x and y substitutes or complements? Why? (1 mark)
8) Use the own price elasticity of demand you calculated above to determine the effect
on the sales of good x, in percentage terms, if the firm were to increase its price by 2%.
(2 marks).
9) If there were a 2% increase in the price of good x, what would be the effect on the
firm's total revenue? Explain. (3 marks)
10) Return to the original situation. This time, suppose the price of good z were to
decrease by 2%. Use the appropriate elasticity measures that you calculated above to
determine how much, in percentage terms, your firm would need to change the price of
x, in order to maintain original sales. (3 marks)
Question 4 Bonus (2 marks)
Is good x a luxury or a necessity good and why?
