4Suppose the preferences of an individual are represented by a quasilinear utility function:U(x, y) = ln(x) + 3ya) Initially, px=1, py=6 and I=102. Then, the price of x increases to 2 (px=2). Calculatethe changes in the demand for x. Please also calculate the substitution and income effectsof the change in px on x. (Hint: since the change in price is not small, you cannot use theSlutsky equation. You need to have numbers instead of functions as the answer.)b) Please also calculate the substitution and income effects of the change in pa on y.c) Instead of doubling to 2, suppose px is only increased by a small amount. Use the Slutskyequation to find the substitution and income effects of the change in the price of x on x.Compare your result to (a). Explain why there's no income effect of the change in px on x.Show your result on an indifference curve.d) Use the Slutsky equation to find the substitution and income effect of the change inPx on y. Compare your result to (b).

Answered: 4 Suppose the preferences of an…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2. Ping receives a weekly allowance to purchase soda (x) and juice (y) at school. His preferences over these two goods can be represented by the utility function U(x,y) =0.5x+ 5lny where x represents the number of cans of soda and y represents the number of juice boxes. a) Given his preferences find his Marshallian demand functions for soda (x) and juice (y). b) Suppose that the price of a can of soda is $1.5 and that Ping has $30 to spend on soda and juice. Write Ping's demand curve for juice (y). Illustrate his demand curve. c) Suppose that the price of a box of juice is $1 (the price of soda and income remain $1.5 and $30, resp.). Use your demand functions to find his best bundle. In an indifference curve diagram illustrate his best bundle at these prices. For the remainder of the question assume that Ping's allowance (income) rises to $36 per week and the prices of the two goods are unchanged at Px= $1.5 and Py= $1. d) Use your demand functions to find his new best bundle. e)…
2)Ben is choosing between cookies and soda. Denote the marginal utility of cookies is MUc, and the marginal utility of soda is MUs. Which of the following relationship is true regarding the marginal utility of substitution (MŘS) of cookie in terms of soda? A) MRS= MUc B) MRS = MUS C) MRS = MUS / MUC D) MRS = MUc / MUs
3. Consider the following utility function: U = 5 x1 + 2 x2 Also consider the following bundles: A=(6, 6) B=(8, 4) C=(4,11) D=(7, 9) E=(9, 3) If x1=20, how much of x2 does the consumer has to consume to obtain a utility level of 150? 50 300 170 25
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Suppose the preferences of an individual are represented by a quasilinear utility function: U(x, y) = In(x) + 3y a) Initially, Px=1, Py=6 and 1=102. Then, the price of x increases to 2 (Px=2). Calculate the changes in the demand for x. Please also calculate the substitution and income effects of the change in Px on x. (Hint: since the change in price is not small, you cannot use the Slutsky equation. You need to have numbers instead of functions as the answer.) B)Please also calculate the substitution and income effects of the change in Pr on y. C) Instead of doubling to 2, suppose Px is only increased by a small amount. Use the Slutsky equation to find the substitution and income effects of the change in the price of x on x. Compare your result to (a). Explain why there's no income effect of the change in Pa On X. Show your result on an indifference curve. d) Use the Slutsky equation to find the substitution and income effect of the change in Px on y. Compare your result to (b).
8
Peter's preferences over two goods, x and y, are represented by the utility function u(x, y) = y + 2x. a) Peter is currently consuming bundle A = (2,4) with 2 units of good x and 4 units of good y. Calculate his current level of utility from consuming this bundle. b) Write the expression the indifference curve representing Peter's current level of utility (i.e., the one you found in part (a). Next draw this indifference curve. c) By looking at the indifference curve you drew in part (b), answer the following questions: Does Peter like good x? Good y? Explain. What can you say about the marginal rate of substitution of good x for y, MRSxy? Is it positive? Negative? Constant? Increasing? Decreasing? Interpret/explain your answer in terms of the tradeoffs Peter is willing to make between goods to keep the same utility level. d) On the same graph you drew in part (b), draw the indifference curve for a utility level of 10. Plot and label in the graph bundles B = (1,2), C = (1,6), and D =…
12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.
Please tell me which of the multiple choices in question 1.6)1.7)1.8) are correct.State only the correct ones please. 1.6) The marginal rate of substitution (MRS) can be defined as: Select one or more: a. The amount of one good that the consumer is willing to trade for one unit of the other. b. The ratio of the amounts of two goods. c. The change in the consumer’s utility when one good is substituted for another. d. The absolute value of the slope of the indifference curve. 1.7) (SEE ATTACHED PICTURE) The diagram shows that: Select one or more: a. If Angela works 24 hours a day she can still survive. b. There is a technically feasible allocation where Angela does not work. c. A new technology that produced more grain would give a larger technically feasible set. d. If Angela needed less grain to survive the technically feasible set would be smaller.
For the utility function, U = 2x1/2 + y What are the income and substitution effect of price changes in Px and Py respectively?

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