In this chapter, we began by considering the impact of an increase in the price of gasoline on George Exxon who owns a lot of gasoline. In this exercise, assume that George and I have exactly the same tastes and that gasoline and other goods are both normal goods for us.
A. Unlike George Exxon, however, I do not own gasoline but simply survive on an exogenous income provided to me by my generous wife.
(a) With gallons of gasoline on the horizontal and dollars of other goods on the vertical, graph the income and substitution effects from an increase in the price of gasoline.
(b) Suppose George (who derives all his income from his gasoline endowment) had exactly the same budget before the price increase that I did. On the same graph, illustrate how his budget changes as a result of the price increase.
(c) Given that we have the same tastes, can you say whether the substitution effect is larger or smaller for George than it is for me?
(d) Why do we call the change in behavior that is not due to the substitution effect an income effect in my case but a wealth effect in George Exxon’s case?
B. We assumed the utility function u(x1,x2) = x10.1 x20.9 for George Exxon as well as an endowment of gasoline of 1000 gallons. We then calculated substitution and wealth effects when the price of gasoline goes up from$2 to $4 per gallon.
(a) Now consider me with my exogenous income I = 2000 instead. Using the same utility function we used for George in the text, derive my optimal consumption of gasoline as a function of p1 (the price of gasoline) and p2 (the price of other goods).
(b) Do I consume the same as George Exxon prior to the price increase? What about after the price increase?
(c) Calculate the substitution effect from this price change and compare it to what we calculated in the text for George Exxon.
(d) Suppose instead that the price of “other goods” fell from$1 to 50 cents while the price of gasoline stayed the same at $2. What is the change in my consumption of gasoline due to the substitution effect? Compare this to the substitution effect you calculated for the gasoline price increase above.
(e) How much gasoline do I end up consuming? Why is this identical to the change in consumption we derived in the text for George when the price of gasoline increases? Explain intuitively using a graph.