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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?

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Answer:

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

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