Question

In: Economics

Suppose John has an income of $300 and spends his income to purchase two goods (X...

Suppose John has an income of $300 and spends his income to purchase two goods (X and Y ). Price of Y is $5 and price of X is $10. Furthermore, John always consumes 2 units of Y with 1 unit of X. (a) How many units of X and Y should John consume in order to maximize his utility? (b) Suppose that the price of X goes up to $15 (income and price of Y are the same). How many units of X and Y should John consume in order to maximize his utility? (c) Plot the budget constraints and indi§erence curves for parts (a) and (b) on the same graph. Clearly label the equilibrium points as "A" for the 5 equilibrium in part (a) and "B" for the equilibrium in part (b). Discuss the results in terms of the income and substitution effects

Solutions

Expert Solution

This is a situation of complementary goods. In complementary goods there is no substitution effect, only changes happen due to income effect. Because in complementary goods, both goods are consumed together in a fixed ratio.

It is given that he consumes 2 units of y with one unit of x. This can be seen as the worth of x is twice the worth of y. So it's utility function is

u(x,y) = min(2x,y)

2x = y

Therefore, Slope will be -2

All my calculations and graph are attached below:

Rahul Sunny answered 1 year ago
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