Assume that the aggregate demand equation for a good has been estimated to be Q
ID: 1167771 • Letter: A
Question
Assume that the aggregate demand equation for a good has been estimated to be Q = 50 – 2P + PZ + 4Y. Q is the quantity demanded, P is the price of the good in dollars per unit, PZ is the price of another good in dollars per unit, and Y is average consumer income in thousands of dollars (that is, when Y equals 10, the average consumer has $10,000 in income).
a. What is the price elasticity of demand when P equals 10, PZ is 20, and Y is 20?
b. What is the cross price elasticity due to a change in the price of good Z when PZ equals 20, P equals 10, and Y is 20?
c. What is the income elasticity of demand when P equals 10, PZ is 20, and Y is 20?
Explanation / Answer
Ans)
Q = 50 – 2P + PZ + 4Y
a) P = 10, PZ = 20, and Y = 20
Q = 50 – 2*10 + 20 + 4*20
Q = 130
Price Elasticity of demand = (P*Q) / (Q* P)
dQ/dP = -2
Ep = 10*(-2)/130 = - 0.1538
b) PZ = 20, P = 10, and Y = 20
Q = 50 – 2*10 + 20+ 4*20
Q = 130
Cross Price Elasticity of demand = (PZ *Q) / (Q* PZ )
c) P = 10, PZ = 20, and Y = 20
Q = 50 – 2*10 + 20 + 4*20
Q = 130
Income Elasticity of demand = (Y*Q) / (Q* Y)
dQ/dY = 4
Ey = 20*(4)/130 = 0.6154