Question

Tracy consumes dress shoes​ (D) and casual Crocs​ (C). Her marginal utility from consuming casual Crocs is MUC = 20DC and her marginal utility from consuming dress shoes is MUD = 10C^2. Her annueal shoe allowance is $450 which she spends only on dress shoes and crocs. If she pays $50 for a pair of dress shoes $25 for a pair of Crocs, what is her optimal consumption bundle?

(I need help with the math part. Does this employ calculus? Please include notes. Thank you :))

Answer 1

Tracy's marginal utility from consuming casual Crocs is MUC = 20DC and her marginal utility from consuming dress shoes is MUD = 10C^2. This will be used to find the MRS which is -MUC/MUD and so MRS = -20DC/10C^2. This is simplified to -2D/C.

Her annueal shoe allowance is $450 which she spends only on dress shoes and crocs. This is her budget and the prices are PD = $50 for a pair of dress shoes and PC = $25 for a pair of Crocs.

Optimal bundle has Indifference curve tangent to the budget line, At the point of contact, slope of Indifference curve is equal to the slope of the budget line. Here we see that budget equation is 450 = 25C + 50D. Hence the slope of the budget line is -25/50 or -1/2.

At the optimal bundle, |MRS| = |slope of the budget line|

2D/C = 1/2 or C = 4D

Use this relation in budget line

450 = 25*4D + 50D

450 = 150D

D* = 3 and C = 4D = 4*3 = 12

The optimal bundle is 3 pairs of dress shoes and 12 pairs of Crocs.