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Suppose a consumer has an income of $30 that is spent on two goods: X and Y. The price of good X is $1.00 and the price of good Y is $3.00. Which of the following bundles of X and Y lie on the individual’s budget constraint?

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Related questions

A consumer has preferences over two goods: x and y. Three bundles, which all lie on the same indifference curve for this consumer, are shown in the following table.

Bundle

x

y

A

2

8

B

2

2

C

6

2


Which of the following statements regarding these bundles is correct?

The goods are perfect substitutes for this consumer.

The goods are perfect complements for this consumer.

These bundles violate the property that indifference curves are bowed inward.

These bundles violate the property that indifference curves do not cross.

Suppose that there are two goods (X and Y). The price of X is $2 per unitu, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.8Y^.2

Consumer A has an income of $100, and Consumer B has an income of $300.

1. Derive the marginal utlities of goods X and Y for consumer A


2. Derive the marginal utilities of goods X and Y for consumer B


3. Set consumer A's MRS equal to the price ratio. Then use the budget constraint to solve for her optimal bundle


4. Set consumer B's MRS equal to the price ratio. Then use the budget contraint to solve for his optimal consumption bundle.


5. Calculate the MRS for each consumer at their optimal consumption bundles.


6. Suppose that there is another conusmer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's MRS at her optimal consumption bundle? Why?


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 571Total 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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