# Calculating 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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#### Solution Preview

Please refer attached file for better clarity of tables.

Good Total Utility of X Total Utility of Y Marginal Utility* MU per dollar spent

TUx TUy MUx MUy MUx/Px Muy/Py

1 20 45 20 45 0.50 0.75

2 38 78 18 33 0.45 0.55

3 54 108 16 30 0.40 0.50

4 68 135 14 27 ...

#### Solution Summary

Solution depicts the steps to calculate the optimal bundles of consumption subject to given levels of budget.

Calculating the Optimal Bundle of Consumption

I need some help in answering the questions about this case study:

U = A(D^1/3 * C^2/3)

Doughnuts are $5

Cookies are $20

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