Tracy consumes dress shoes (D) and casual Crocs (C). Her marginal utility from consuming casual Crocs is MU Subscript Upper CMUCequals=20DC and her marginal utility from consuming dress shoes is MU Subscript Upper DMUDequals=10Upper C squaredC2. Her annual shoe allowance is $450450 , which she spends on only dress shoes and Crocs. If she pays $5050 for a pair of dress shoes and $2525 for a pair of Crocs, what is her optimal consumption bundle?

The optimal bundle is 6 pairs of dress shoes and 3 pairs of Crocs.

Explanation:

From the question,

Allowance (M) = $450; Price of dress shoes, Pd = $50; Price of crocs, Pc = $50

Note: MRS-price ratio, MUC - marginal utility from consuming casual Crocs, MUD - marginal utility from consuming dress shoes

Optimal bundle is determined where MRS = Price ratio

MRS = MUC/MUD = 20DC/10C2 = 2D/C

Price ratio = Pd/Pc = 50/50 = 1

So, 2D/C = 1

Therefore, C = 2D

Budget constraint: M = Pd*D + Pc*C

So, 50D + 50 * (2D) = 450

50D + 100D = 150D = 450

So, D = 450/150 = 3

C = 2D = 2*3 = 6