Question

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 equilibrium in part (a) and "B" for the equilibrium in part (b). Discuss the results in terms of the income and substitution e§ects.

Thats alle the information I received

Answer 1

Consider the image above for the graphical and numerical solution to the question. In part a) optimal bundle is at x=15, y=30 and in part b) optimal bundle is at x=12, y=24. The entire change is comprised of income effect, there is no substitution effect in this case.