The following demand for potatoes in the United States was estimated for 1959-19

Question

The following demand for potatoes in the United States was estimated for 1959-1973 period:

            Q = 163.6 – 17.7Px + 9.3I

Where Q is the annual consumption of potatoes in pounds per capita, or per person; Px is the average price in dollars per 100 pounds of potatoes; and I is the average per capita income in thousands of 1958 dollars. If we imagine that this year, Px = $3 and I = $2.344, calulate:
(a) The sales of potatoes this year.
(b) The elasticity of sales with respect to Px and I.
(c) What would the sales be next year if Px was reduced by 15% and I was increased by 20%?
(d) How much would income have to decrease if sales of potatoes were to be 10% lower next year and price remained constant?

Explanation / Answer

a) Q = 163.6 - (17.7* 3 ) + (9.3 * 2.344)

Q = 163.6 - 53.1 + 21.8

Q = 132.3

the sale of potatoes this year is 132.3

b) elasticity of sales with repsect to PX  

ed = -17.7 * 3 / 132.3

ed = -0.4

elasticiy of sales with respect to I.

ed = 9.3 * 2.344/132.3

ed = 0.16

c) PX reduced by 15% so PX becomes = $2.55

I increase by 20%, then I becomes= 2.8128

Q = 163.6 - 45.135 + 26.15

Q = 144.6

d) 130.14 = 163.6 - 45.135 +9.3I

130.14 = 118.465 +9.3I

11.675 = 9.3I

I = 1.255

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