Suppose a consumer with income m = 12 has preferences that are represented by the utility function u(x1, x2) = x^3,x. The prices for goods 1 and 2 are p1 = 1 and p2 =1.
a. What is the equation for the consumer’s budget line?
b. What is the equation that describes the consumer’s MRS?
c. Write the tangency condition for this problem.
d. Solve for this consumer’s optimal bundle and then illustrate the optimal choice bundle, the budget set, and the indifference curve passing through the optimal bundle. Make sure to fully and appropriately label the diagram.
e. Now suppose that income increases to m = 15. Solve for the new optimal bundle and draw a new diagram containing both the original optimal bundle and the new optimal bundle.