Calculating the Optimal Bundle of Consumption

U = A(D^1/3 * C^2/3)
Doughnuts are \$5
Income is \$200

a. Assume that A= 1 for Janet’s utility function (above). Calculate the marginal utility of doughnuts; the marginal utility of cookies;
b. Calculate the marginal rate of substitution of cookies for doughnuts (MRSC, D) for Paul’s utility function.
c. Now, assume doughnuts and cookies can be sold in whole or in half packs. Assume also that the price and income levels of the two commodities are as provided above. Prove that the utility maximizing bundle for Janet will be 14 packs of doughnuts and 6.5 packs of cookies

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Solutions:
a. Assume that A= 1 for Janet’s utility function (above). Calculate the marginal utility of doughnuts; the marginal utility of cookies;
U = A(D^1/3 * C^2/3)

Marginal Utility of doughnuts=MUD=dU/dD=A*(1/3)*D^(1/3-1)*C^(2/3)
Put A=1
MUD=(1/3)*D^(-2/3)*C^(2/3)

Marginal Utility of …

Solution Summary
This solution depicts the steps to estimate the optimal bundle of consumption in the given case with step-by-step calculations and all formulas shown.

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