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Calculating the Optimal Bundle of Consumption

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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.

\$2.19

Find the optimal bundles of consumption.

Assume that an individual consumes two goods, X and Y. The total utility of each good is independent of the rate of consumption of the other good.

The price of X and Y are \$40 and \$60 respectively. Use the following table of total utilities to answer the following questions.

Good Total Utility of X Total Utility of Y
1 20 45
2 38 78
3 54 108
4 68 135
5 80 159
6 90 180

a. The marginal utility of the fourth unit of Y is _.
b. The marginal utility of the fifth unit of X is _.
c. The marginal utility per dollar spent on the third unit of X is _.
d. The marginal utility per dollar spent on the second unit of Y is _.
e. If the consumer has \$420 to spend, _ unit of X and _ units of Y maximize utility subject to the budget constraint. Explain.
f. If the consumer has \$220 to spend, _ units of X and _ units of Y maximize utility subject to the budget constraint. Explain.

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