# arc price elasticity of demand

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1. In 1998 the fare on Chicago's transit system was 60 cents per ride. This resulted in 711.6 million trips being taken on the system. In 1999 the fare was increased to 80 cents and ridership declined to 692.4 million trips.

a. Compute the arc price elasticity of demand for transit ridership in Chicago assuming that all other factors influencing demand remained constant during this period.

b. Based on your answer to part (a), do you believe the fare increase was a rational action for the Chicago Transit Authority?

c. What other factors do you feel may have had an impact on ridership during this period? Do you believe the decline in ridership experienced in 1999 tends to overstate or understate the actual impact of the fare increase?

d. In 2000 the fare increased to 90 cents and ridership declined to 640 million trips. Compute the arc price elasticity between 1999 and 2000. How can you account for the differences between the 1998-1999 elasticity coefficient and the 1999-2000 elasticity coefficient?

2. The demand for haddock has been estimated as28

log Q = a + b log P + c log I = d log Pm

where Q = quantity of haddock sold in New England

P = price per pound of haddock

I = a measure of personal income in the New England region

Pm = an index of the price of meat and poultry

If b = -2.174, c = .461, and d = 1.909,

a. Determine the price elasticity of demand.

b. Determine the income elasticity of demand.

c. Determine the cross price elasticity of demand

d. How would you characterize the demand for haddock?

e. Suppose disposable income is expected to increase by 5 percent next year. Assuming all other factors remain constant, forecast the percentage change in the quantity of haddock demanded next year.

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#### Solution Summary

Compute the arc price elasticity of demand for transit ridership in Chicago assuming that all other factors influencing demand remained constant during this period.

Calculating Arc Price Elasticity of Demand

Arc Price Elasticity. Assume that amazon.com cut the price on a 1.10 ct Princess Cut Diamond Solitaire engagement ring from $4,500 to $2,500, and sales rose from 50 to 75 units per week.

A. Calculate the implied arc price elasticity of demand.

B. Is a further price decrease warranted? Why or why not?