Interpreting a (Linear) Demand Function

Interpreting a (Linear) Demand Function

 You can work in groups on this if you want, but be sure you all understand it. For this assignment, you can turn in one assignment for up to three people – just be sure everyone’s names on it.

Your research assistant has estimated demand for Coke as:

QC = 26.17 – 3.98PC + 2.25PP + 2.6AC – 0.62AP + 0.99Y + 9.58S

 where:

QC = quantity demanded of Coke (ten million cases)

PC = price of Coke (dollars per ten cases)

PP = price of Pepsi (dollars per ten cases)

AC = advertising expenditures by Coke (millions of dollars)

AP = advertising expenditures by Pepsi (millions of dollars)

Y = per capita disposable income in the U.S. (thousands of dollars)

 S = variable equal to one during spring and summer and 0 otherwise.

 Assume the price of Coke is currently $12.96 (per ten cases) and the price of Pepsi is currently $8.16 (per ten cases). Coke spends $5.98 million on advertising and Pepsi spends $5.28 million. Per capita disposable income is currently $20,630 (so 20.63 in thousands), and it is August (summer).

1. Find the demand curve for Coke, write it as an equation, and draw it on a graph with the intercepts labeled.

2. Based on this information, what is the current quantity demanded of Coke?

3. What is the elasticity of demand for Coke at the price of $12.96?

4. If the price of Coke increased by 10%, by what percent would quantity demanded change? Is the demand for Coke elastic or inelastic? Given this increase in price, would revenue for Coke increase or decrease?

5. If the price of Pepsi increased by 10%, by what percent would quantity demanded of Coke change? Are Coke and Pepsi substitutes or complements?

 6. If disposable income increased by 10%, by what percent would quantity demanded of Coke change? Is Coke a normal or inferior good?