Question

Suppose a firm has an estimated general demand function for good X is given by:

Q = 200,000 -500P + 1.5M – 240Pr

Where P = price of good X, M is the average income of the consumers who buy good X, and Pr is the price of a related good. Suppose that the values of P, M and Pr are given by $200, $80,000, and $100 respectively.

An increase in the price of good X by 5% will

Decrease quantity demanded of good X by 3%

Increase quantity demanded of good X by 2.55%

Increase quantity demanded of good X by 3%

Decrease quantity demanded of good x by 2.55%

Suppose a firm has an estimated general demand function for good X is given by:

Q = 200,000 -500P + 1.5M – 240Pr

Where P = price of good X, M is the average income of the consumers who buy good X, and Pr is the price of a related good. Suppose that the values of P, M and Pr are given by $200, $80,000, and $100 respectively.

A decrease by income of 5%

will increase quantity demanded by 3.05%

Suppose a firm has an estimated general demand function for good X is given by:

Q = 200,000 -500P + 1.5M – 240Pr

Where P = price of good X, M is the average income of the consumers who buy good X, and Pr is the price of a related good. Suppose that the values of P, M and Pr are given by $200, $80,000, and $100 respectively.

The cross-price elasticity of demand is:

-1.12

-.21

-.12

-1.4

will increase quantity demanded by .6%

will decrease quantity demanded by 3.05%

will decrease quantity demanded by .6%

Answer 1

1. Decrease quantity demanded of good x by 2.55%
(Q = 200,000 -500P + 1.5M – 240Pr = 200,000 - 500(200) + 1.5(80,000) - 240(100) = 200,000 - 100,000 + 120,000 - 24,000 = 196,000
dQ/dP = -500
Own price elasticity = (dQ/dP)*(P/Q) = (-500)*(200/196,000) = -.51
So, as price increase by 5%, change in quantity demanded = (-.51)*(5%) = -2.55%)

2. will decrease quantity demanded by 3.05%
(dQ/dM = 1.5
Income elasticity = (dQ/dM)*(M/Q) = (1.5)*(80,000/196,000) = .61
Decrease in income by 5% changes quantity demanded by (-5%)*(.61) = -3.05%)

3. -.12
(dQ/dPr = -240
So, cross price elasticity = (dQ/dPr)*(Pr/Q) = (-240)*(100/196,000) = -.12)