Problem Set 1:

1. The demands for substitute products (like oil and coal) depend negatively on their own price and positively on the price of the other product. We measure the responsiveness of consumption of a good to its own price by the own price elasticity of demand and its responsiveness to the price of the other product by the cross price elasticity of demand. In particular, the elasticity of demand for product X with respect to the price of product Y measures the percentage increase in the demand for product X for each 1% increase in the price of product Y (i.e., εXY = ΔX/ΔPY).

In general, changes in one market can have a significant effect on the other market as consumers substitute between products. The demand curve of X can therefore be represented by

ΔQX = εDXXΔPX + εDXYΔPY

The supply curve of X can be written as

ΔQX = εSXXΔPX

For the analysis below assume the following elasticities and provide quantitative answers if possible.

Own price elasticity of demand for oil = -0.2

Elasticity of demand for oil with respect to the price of coal = +0.1

Own price elasticity of demand for coal = -0.4

Elasticity of demand for coal with respect to the price of oil = +0.2

Elasticity of supply of coal = +1

Elasticity of supply of oil = +1

(a) Now assume that the government institutes a 4% tax on oil. How will the tax affect the prices of coal and oil? What will happen to coal and oil consumption?

(b) If prior to the tax, coal account for 1/3 of expenditures on energy and oil accounts for 2/3 of energy expenditures, calculate the changes in the overall price and consumption of energy. What is the elasticity of demand for energy implied by these numbers?

(c) Based on your calculation above, do you think the tax on oil is good or bad for the environment?

2. Assume that independent research discovers that consumption of your company's distilled water (at a bottle per day, instead of drinking tape water because of water pollution) reduces the risk of infectious waterborne diseases by about 4% and that other research has established that people are willing to pay about $2,000 per year to eliminate their risk of infectious waterborne diseases. Assume that sales of distilled water are currently 500,000,000 bottles per year.

(a) How much would widespread knowledge of this research increase the demand for your company's product if a bottle of distilled water sells for $2 and the elasticity of demand for your company's distilled water is -2?

(b) How much do you estimate that you could increase the price per bottle and still sell as many after people learn about the health benefits of your distilled water?

(c) How much would your company be willing to spend on advertising to inform people about the heath advantage of your product?