Consider a hypothetical consumer with preferences over two products x and y represented by the utility function U(x; y) = xy. Assume px = 4; py = 4; I = 200:
1. Draw her budget line. Algebraically find out her optimal consumption bundle. What is her level of utility at the optimal consumption bundle? Indicate the optimal point on the budget line and draw a hypothetical indifference curve that is tangent to the budget line at the optimal point.
2. Suppose that price of x decreases, but the price of y and her income remain unchanged. The new prices and income are: px = 1; py = 4; I = 200: Draw her new budget line. Algebraically find out her (new) optimal consumption bundle. What is her level of utility at the optimal consumption bundle? Is she better off or worse off relative to part (1)? Indicate the optimal point on the budget line and draw a hypothetical indifference curve that is tangent to the budget line at the optimal point.
3. On a single diagram with budget lines and indifference curves, indicate the optimal consumption points that you have obtained in parts (1) and (2).
4. Now suppose $100 is taken away from the consumer (to offset the effect of the price decrease). The new prices and income are: px = 1; py = 4; I = 100: Draw her new budget line. Algebraically find out her (new) optimal consumption bundle. What is her level of utility at the optimal consumption bundle? Is she better off or worse off relative to part (1)? Indicate the optimal point on the budget line and draw a hypothetical indifference curve that is tangent to the budget line at the optimal point.
5. On a single diagram with budget lines and indifference curves, indicate the optimal consumption points that you have obtained in parts (1) and (4).