Question

1) A U.S. Department of Agriculture study of the demand for food products showed that the price elasticity of demand for potatoes is -0.42; the elasticity of demand for potatoes with respect to the price of tomatoes is 0.09; and the income elasticity of demand for potatoes is 0.10.

a. If consumer incomes rise by 10%, by what percentage will the quantity of potatoes demanded change? Will it rise or fall? Show your work.


b. If consumer incomes rise by 10% (as in the last question), would the share of consumer income spent on potatoes rise, or would it fall? Calculate an estimate of the percentage change in the share of income spent on potatoes as a result of a 10% increase in income. Explain your reasoning.

c. Based on the figures above, are potatoes and tomatoes complements, or are they substitutes? Why? Explain your reasoning.


d. If the price of tomatoes rises by 10%, by what by what percentage will the quantity of potatoes demanded change? Will it rise or fall? Show your work.


e. Suppose you’re working as an economist with the Idaho Potato Growers Institute, and your boss asks you to predict the future growth rate of potato sales. You estimate that consumer’s incomes will grow at a rate of 2% per year in the future, and that the price of potatoes will fall by 1% per year. By what percentage do you estimate that the sales of potatoes will change each year in the future? Will it rise or fall? Show your work.

Sketch a graph of the demand for potatoes to illustrate the one yr change in sales of potatoes based on part (e)

Answer 1

a. Income elasticity of demand for potatoes = Percentage change in quantity demanded for potatoes/Percenatge change in income

or, 0.10 = Percentage change in quantity demanded for potatoes/10

or, Percentage change in quantity demanded for potatoes = 0.10 * 10

or, Percentage change in quantity demanded for potatoes = 1%

Thus, with 10% increase in income, quantity demanded for potatoes increases by 1%.

b. With 10% increase in consumer income, quantity demanded for potatoes increases by 1%.

Now, price elasticity of demand for potatoes = Percentage change in quantity demanded for potatoes/Percentage change in price of potatoes

or, -0.42 = 1/Percentage change in price of potatoes

or, Percentage change in price of potatoes = - 1/0.42

or, Percentage change in price of potatoes = -2.4%

Thus, with increase in income by 10%, quantity demanded for potatoes increases by 1% while price of potatoes fall by -2.4%. As a result, total expenditure on potatoes fall by -2.4*1 = -2.4%.

Here, percentage change in income share on potatoes is -2.4%.

c. As the cross-price elasticity of demand for potatoes due to change in price of tomatoes is positive (+0.09), potatoes and tomatoes are substitutes. (Cross-price elasticity for complements is negative)

d. Cross-price elasticity of demand for potatoes = Percentage change in quantity demanded for potatoes/Percenatge change in price of tomatoes

or, 0.09 = Percentage change in quantity demanded for potatoes/10

or, Percentage change in quantity demanded for potatoes = 0.09 * 10

or, Percentage change in quantity demanded for potatoes = 0.9%

Thus, with 10% increase in price of tomatoes, quantity demanded for potatoes increases by 0.9%.