3. Assume a person has a utility function U = XY, and money income of GH¢ 10,000, facing an initial price of X of GH¢ 10 and price of Y of GH¢ 15. If the price of X increases to GH¢15, answer the following questions: a. What was the initial utility maximizing quantity of X and Y? What is the new utility maximizing quantity of X and Y following the increase in the price of X? c. Calculate the substitution effect and the income effect on X of this increase in the price of X using the Slutsky analysis. b.

3. Assume a person has a utility function U = XY, and money income of GH¢ 10,000, facing an initial price of X of GH¢ 10 and price of Y of GH¢ 15. If the price of X increases to GH¢15, answer the following questions: a. What was the initial utility maximizing quantity of X and Y? What is the new utility maximizing quantity of X and Y following the increase in the price of X? c. Calculate the substitution effect and the income effect on X of this increase in the price of X using the Slutsky analysis. b.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.10P

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Similar questions

If a 10 decrease in the price of one product that you buy causes an 8 increase in quantity demanded of that product, will another 10 decrease in the price cause another 3 increase (no more and no less) in quantity demanded?
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Let the following table represents the total utility of a given consumer, in the cardinal utility approach. Q 1 2 3 4 5 Tux 8 14 18 20 20 Tuy 6 10 13 15 16 Mux Muy Mux/px Muy/py D) Assuming the consumer has any amount of money (enough budget) how many of X and Y should the consumer buy, to maximize utility? E) What is the total utility of X and Y? F) Let now price of X is 4 birr per unit and price of Y is 2 birr per unit and budget of the consumer for consumption of X and Y is 20 birr. Given budget constraint how many of X and Y should the consumer buy to maximize utility? G) What are the total utility of X and Y
5. Consider a consumer whose utility function isu(x,y) = sqrt(xy) (MRS(x,y)=y/x)a. Assume the consumer has income $120 and initially faces the prices px = $1 and py = $1. Howmuch x and y would they buy? Draw the budget constraint and the demands. b. Next, suppose the price of x were to increase to $2. How much would they buy now? Draw thisin the same figure.c. Decompose the total effect of the price change on demand for x into the substitution effect and theincome effect. That is, determine precisely how much of the change is due to each of thecomponent effects. (Hint: See the lecture notes for the two properties that determine the locationof “z”, the reference point for distinguishing the income and substitution effects.)
1. Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = lnx + 2lny (MUx = 1/x, MUy = 2/y). a. Derive his demand functions for x and y. Are they homogeneous in income and prices? b. Assuming I = $60 and px = $1, graph his demand curve for y. c. Repeat part (b) for the case in which px = $2
1. Suppose that a consumer’s utility function for two goods (X and Y) is U(X,Y) = 10X^0.5 + 2Y , with MUx = 5X-0.5 and MUy = 2. The price of good X is $5 per unit, the price of good Y is $10 per unit, and the income is $275. a. Find the utility maximizing quantities of X and Y. b. If instead, the price of good Y is $20 per unit, how does your answer change?
22. Peanut butter (PB) sells for 10 dollars per pound and Oysters (O) sell for 50 dollars perpound. Suppose Pat buys 5 pounds of peanut butter and one pound of oysters each month.With this consumption bundle, his MRSP B,O = 3. Which of the following is true (assumingPat’s preferences satisfy all the basic assumptions of consumer theory)?(a) Pat could increase his utility by buying more oysters and less peanut butter.(b) Pat could increase his utility by buying more peanut butter and less oysters.(c) Pat could increase his utility by buying more peanut butter and more oysters.(d) Pat could increase his utility by buying less peanut butter and less oysters.
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