Question

. The demand for good X is given by this equation:
Q x= 1.0–2.0Px +0.8I +1.5P –3P z+ 1.0A
where PX, PY, and PZ represent the prices of goods X, Y, and Z; I measures income per capita; and A is advertising. Currently:
P x = 2.00, P y =2.50, P z= 1.00, I= 4, and A= 3.05.
a. Is good X a necessity or a luxury good? How do you know? (4 marks)
b. Calculate the cross elasticity of demand for X with respect to the price of
good Z. Are goods X and Z substitutes or complements? (4 marks)
c. Calculate the advertising elasticity of demand for X. Interpret your answer. (4
marks)
d. What kind of change in the price of X would you recommend if the firm is interested in maximizing revenue? (8 marks)

Answer 1

QX =1.0–2.0PX +0.8I+1.5PY –3PZ+1.0A Where PX, PY, and PZ represent the prices of goods X, Y, and Z; I measures income per capita; and A is advertising. PX =2.00,PY =2.50,PZ =1.00,I=4,andA=3.05.
A.Qx = 1 - 2*2 + 0.8*4 + 1.5*2.5 - 3*1 + 1*3.05 = 4 units It is a luxury good, as its quantity is only 4 units.
B. So, Ex,z = k*Pz/Qx = -2*1/4 = -0.5, where k is koefficient before Px as the derivative of ∆Q/∆P.
Two goods that complement each other show a negative cross elasticity of demand: as the price of good Y rises, the demand for good X falls. So, x and z are complements.
C. So, Ed = k*A/Qx = -2*3.05/4 = -1.525, where k is koefficient before Px as the derivative of ∆Q/∆P, so the advertising is elastic as Ed < -1.
D.As the advertising is elastic, the decrease in price will increase the revenue, as the change in quantity demanded will be higher than the change in price.