Question

You can get your electricity from two different sources: Solar (S) or Natural Gas (G). You see solar and natural gas as perfect substitutes, and are indifferent between the two sources. Right now, electricity from natural gas is $0.10 per unit and solar is $0.25 per hour. You have $50 per month to spend on electricity.

1 Intuitively, given your preferences and prices, which source would you use?

2 Based on your preferences, what is your utility function?

3 Graph your utility maximizing choice.

4 If the State of Massachusetts wanted to encourage you to switch to solar

electric, how big a tax would it need to charge on natural gas?

5 How big are the income and substitution effects from this tax?

Answer 1

1)

Solar and Natural Gas are perfect substitutes. Since natural gas has a lower price, I will use it only

2)

Since both are perfect substitutes the utility function would be U(s,n) = s + n

3)

Since both are perfect substitutes the indifference curve(CB) will be a straight line with slope = 1

The budget line(AB) will also be a straight line with slope 0.1/0.25 = 0.4

We will have a corner solution as point B, where the consumer is consuming only natural gas.

4)

For a consumer to switch to solar electricity, the price of solar electricity must be lower than the price of natural gas. Thus a tax of at least $0.16 must be imposed on natural gas.