Question

The equation for a demand curve has been estimated to be Q = 100 - 10P + 0.5Y, where
Q is quantity, P is price, and Y is income. Assume P = 7 and Y = 50.
a. Interpret the equation.
b. At a price of 7, what is price elasticity?
c. At an income level of 50, what is income elasticity?
d. Now assume income is 70. What is the price elasticity at P = 8?.

5. Mr. Smith has the following demand equation for a certain product: Q = 30 - 2P.
a. At a price of $7, what is the point elasticity?
b. Between prices of $5 and $6, what is the arc elasticity?
c. If the market is made up of 100 individuals with demand curves identical to Mr. Smith’s,
what will be the point and arc elasticity for the conditions specified in parts a and b

Answer 1

The equation for a demand curve has been estimated to be Q = 100 - 10P + 0.5Y. Assume P = 7 and Y = 50.

a. There is a direct relationship between quantity demanded and income and inverse relationship between quantity demanded and price.

b. At a price of 7 price elasticity is: Ed = -b*P/Q = -10*7/(100 - 10*7 + 0.5*50) = 1.27.

c. At an income level of 50 income elasticity is: Ei = 0.5*50/(100 - 10*7 + 0.5*50) = 0.45.

d. Now assume income is 70. The price elasticity at P = 8 is: Ed = -10*8/(100 - 10*8 + 0.5*70) = -1.45.

5. Mr. Smith has the following demand equation for a certain product: Q = 30 - 2P.

a. At a price of $7, the point elasticity is: Ed = -b*P/Q = -2*7/(30 - 2*7) = -0.875.

b. At prices of P1 = $5 and P2 = $6 quantities demanded are Q1 = 30 - 2*5 = 20, Q2 = 30 - 2*6 = 18, so the arc elasticity is:

Ed = (18 - 20)/(6 - 5)*(6 + 5)/(18 + 20) = -2/1*11/38 = -0.579.

c. If the market is made up of 100 individuals with demand curves identical to Mr. Smith’s, then the point and arc elasticity for the conditions specified in parts a and b will be the same.