ECO2023 Problem Set 4 - Economics PDF

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ECO 2023 Spring 2016 n

Problem Set 4

1.

Suppose that a consumer’s preferences for goods X and Y are characterized by the utility function U = X 0.5Y 0.5.

A.

Consider the following bundles: (1,1), (2,1), (3,1), (4,1) and (5,1). Calculate the total utility associated with each bundle and the marginal utility of the 2nd, 3rd, 4th, and 5th unit of X. Does the law of diminishing marginal utility hold in the consumption of X?

B.

Calculate the level of utility associated with the bundles (2,5), (3,5), and (2,6), and rank the bundles from mostpreferred to least-preferred by the consumer.

C.

Derive and graph the indifferen ce function associated with the most-preferred b un dle in B.

D.

Considering the indifference function in C, calculate the amount of Y that is sacrificed if consumption of X increases from 1 to 2 units, from 2 to 3 units, from 3 to 4 units, and from 4 to 5 units.

2.

The budget constraint shows the bundles/combinations of goods and services an individual consumer can obtain with a fixed amount of income and exogenously determined prices. Suppose Frank has a weekly income of $200 and spends all of this on goods X and Y priced at $4 and $2, respectively.

A.

Derive an algeb raic expression for Frank’s b udget con straint and depict the b udget con strain t graphicall y. Be sure to properly label both axes.

B.

Calculate the opportunity cost of the 5th , 10th , 15th, and 20th unit of good X. Is the opportunity cost of X increasing? Explain.

C.

Suppose that a quantity discount is available on good X. The first 20 units of good X may be purchased for Px = $4 each, and all units greater than 20 (i.e., the 21st, 22nd, ...., unit) can be purchased at a price of Px = $2. Depict graphically the budget constraint that reflects this quantity discount. Be sure to properly label the axes and indicate the proper values of the intercepts.

D.

Suppose that instead of a quantity discount, a quantity penalty is imposed u pon con sumption of g ood X. Specifically, the first 10 units of good X may be purchased for P X = $4 each, but all units greater than 10 (i.e., the 11th, 12th, ...., unit) must be purchased at a price of P X = $8. Depict graphically the budget constraint that reflects this quantity penalty. Be sure to properly label the axes and indicate the proper values of the intercepts.

3.

Suppose that an individual’s purchases (i.e., the quantity demanded) of gasoline have been completely unaffected by the changes in the price of gasoline that have occurred over the past several weeks. In addition, assume that the individual’s income and the prices of other goods have not changed over this period.

A.

Given the above information, use the consumer choice model (i.e., budget constraints and indifference curves) to show how purchases of gasoline and consumption of (or expenditures on) other goods have been affected by at least 2 increases in the per-gallon price of gasoline from an initial price of P 0per gallon. The quantity of gasoline should be measured along the horizontal axis, and consumption of (or expenditures on) other goods should be measured along the vertical axis.

B.

Considering ‘C’ depict graphically the individual’s demand curve for gasoline over the price range.

C.

W hat is the price elasticity of demand for this individual over the price range used in ‘C’? Either calculate the exact value or thoroughly explain how you arrived at this value.

4.

The table below describes the marginal utility derived by a consumer from units of good X and good Y. Assume that the prices of X and Y are $4 and $3 respectively and that the consumer's income is $17.

U nits of X

MU X

U nits of Y

MUY

0

---

0

---

1

12

1

21

2

8

2

12

3

4

3

6

4

4

4

0

5

0

5

-2

6

-2

6

-6

A.

W hat bundle of X and Y maximizes the consumer’s utility? Show all calculations that lead to your conclusion.

B.

Calculate the maximum total utility derived by the consumer. Also, pick at least one other bundle that does not exceed the individual’s income and confirm that the total utility is less than that derived by the optimal bundle.

5. Utility refers to the: A) relative scarcity of a product B) usefulness of a product C) satisfaction that a consumer derives from a good or service D) rate of decline in a product demand curve 6. The law of diminishing marginal utility states that: A) total utility is maximized when consumers obtain the same amount of utility per unit of each product consumed B) price must be lowered in order to induce firms to supply more of a product C) beyond some point additional units of a given product will yield less and less extra satisfaction to a consumer D) it will take larger and larger amounts of resources beyond some point to produce successive units of a product 7. If total utility is increasing, then marginal utility: A) is positive, but it may be either increasing or decreasing B) may be either positive or negative C) must also be increasing D) will be increasing at an increasing rate 8. Marginal utility can be: A) positive or negative but not zero B) positive, negative, or zero C) positive but not negative D) decreasing but not negative 9. The slope of an indifference curve (also known as the marginal rate of substitution or MRS) measures the: A) consumer's willingness to substitute one product for another such that total utility will remain constant B) total utility received by a consumer when equilibrium is achieved C) extra utility that a consumer derives from successive units of a product D) magnitude of the substitution effect

10. In moving along the budget constraint: A) each point on the line will be equally satisfactory to consumers B) income varies, but the prices of the two goods are constant C) the prices of both products and income are assumed to be constant D) the prices of both products are assumed to vary, but income is constant 11. The slope of the budget constraint reflects the: A) elasticity of demand for the two products B) price ratio of the two products C) amount of the consumer's income D) utility ratio of the two products 12. The consumer choice model indicates that consumer equilibrium (i.e., maximization of utility) occurs: A) where the budget constraint touches the highest possible indifference curve B) where an indifference curve has a slope of 1 C) where any two indifference curves intersect D) at all points where the budget constraint intersects an indifference curve 13. The marginal utility of the final unit of X consumed is 18 and the marginal utility of the final unit of Y consumed is 6. Assuming the individual is maximizing utility, what set of prices would exist for goods X and Y, respectively? A) $2 and $6 B) $6 and $2 C) $3 and $0.33 D) $0.33 and $3 14. To derive an individual’s demand curve for a good using the consumer choice model: A) the prices of the goods and income are simultaneously varied to identify the utility maximizing quantities of goods B) the price of the good is varied and the new utility maximizing quantity of the goods is then identified C) the prices of both goods are varied and the new utility maximizing quantity of goods is then identified D) the price of the good is held constant and the indifference curves are varied to identify the new utility maximization quantity of goods 15. Suppose an individual is maximizing utility, given income and prices. If the individual’s income decreases, then: A) the budget constraint will shift inward, the consumer will move to a new equilibrium along a lower indifference curve, and the level of total utility will increase B) the budget constraint will shift inward, the consumer will move to a new equilibrium along a higher indifference curve, and the level of total utility will decrease C) the budget constraint will shift inward, the consumer will move to a new equilibrium along a lower indifference curve, and the level of total utility will decrease D) the budget constraint will shift outward, the consumer will move to a new equilibrium along a higher indifference curve, and the level of total utility will increase...