Question

1. Sally has preferences represented by the utility function UC, M) = 3 + 61rC M, where C is coffee and M is meals. Her income is S100, and she pays $2 per coffee and S10 per meal a. Distinguish (the concepts of) diminishing marginal rate of substitution from diminishing marginal uty Your answer does not have to be specific to Sally's preferences. (4 points) Use the Lagrangian method to derive Sally's utility maximizing bundle given her budget constraint. Circle your answers. (5 points) Now suppose the price of a meal increases to $20. Redo part b. You are not required to use the Lagrangian method for this part. (4 points) d. b. c. On one graph, depict Sally's utility maximizing bundles using indifference curves and budget lines, both before and after the price of a meal increases. (4 points)

Answer 1

1. Marginal rate of substitution represents the rate at which a consumer will give up an amount of one good with the excess consumption of some different good, while Marginal Utility represents the rate at which the utility of a good changing with the change in quantity of good consumed. MRS diminishes as one good is consumed over other due to a fixed budgetary constraint. Its a relative concept and given by -MU1/MU2, where MUi is marginal utility of good i.

2.

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