Suppose the utility function is U(x,y)=xy². In 2021, Px=1, Py=2. Due to covid, the price of x in 2022 rises toPx=2. Your income is I=150 unchanged in these two years.1. What is the optimal allocation of x and y before the price change?2. What is the optimal allocation of x and y after the price change?3. What are the (approximate) substitution and income effects of this change in prices?

1. Optimal Allocation of x and y Before the Price ChangeGiven:Utility function: U(x,y)=xy2Prices in…

Answered: Suppose the utility function is…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Floyd's utility function is given by U(X,Y)=2XY. MUx=2Y and MUy-2X. The price of good X is Px=2, while the price of good Y is Py = 1. Floyd's income is 1,000. Which of the following is true given that the price of good X falls to 1? The substitution effect for good X results in an increase of X consumption by about 1,043 units and a decrease in Y consumption by about 14 units. The substitution effect for good X results in X consumption of about 250 units. The substitution effect for good X results in X consumption of about 500 units. The substitution effect for good X results in an increase of X consumption by about 250 units and no change in Y consumption.
A consumer is in equilibrium at point A in the accompanying figure. The price of good X is $5. At point A, how many units of good X does the consumer purchase? Suppose the budget line changes so that the consumer achieves a new equilibrium at point B. What change in the economic environment led to this new equilibrium? Is the consumer positively or negatively affected by the price change?
Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is U(x,y) = xy and Donna’s utility function is U(x,y) = x2y where x is strawberries and y is chocolate. Jim’s marginal utility functions are MUX=y and MUy=x while Donna’s are MUX=2xy and MUy=x2. Jim’s income is $100, andDonna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4?
Clarke County High School has $60,000 to spend on computers and other goods so its budget equation is C + X = 60,000, there C is expenditure on computers and X is expenditure on other things. The high school’s preferences can be represented by the utility function ?(?, ?) = ??2, where the marginal rate of substitution is −?/2?. Currently, the high school’s optimal bundle is $20,000 of computers, and $40,000 of everything else.a. Graphically show the school’s budget line, with computers on the x-axis and all other goods on the y-axis. Label intercepts and the current optimal bundle and sketch an indifference curve.b. The State Education Commission wants to encourage “computer literacy” in schools, and so has proposed the following plan: Give a grant of $20,000 to each school in the state, which the school can use only for computers. If the state adopts the plan, add the school’s new budget constraint to the graph above, making sure to label the line and the appropriate intercepts. What…
1.2 Ann and Bob each own 10 bottles of beer and, altogether, they own 20 bags of peanuts. There are no other people and no other goods in the economy, and no production of either good is possible. Using a to denote bottles of beer and y to denote bags of peanuts, Ann's and Bob's preferences are described by the following utility functions: UA (XA, YA) = TAYA and UB (XB, YB) = 2xB+ YB. In each of the following cases, determine the market equilibrium price ratio and allocation and depict the equilibrium in an Edgeworth box diagram. (a) Bob owns 20 bags of peanuts and Ann owns no peanuts. (b) Bob owns 15 bags of peanuts and Ann owns 5 bags. (c) Ann owns 20 bags of peanuts and Bob owns no peanuts.
Can you help me answer this macroeconomics theory question
A consumer is choosing between magazines and books. His set of čonsumer optimums are shown on the graph to the right. 50 Consumer income allocated for these two goods is equal to $150. The price of magazines (P,) is equal to $5.00. 45- 40 How do these changes in the price of books affect the demand for magazines? 35 demand remains constant 30- We can consider books and magazines to be goods. 25- 20- 15- PCC substitute 10- 5- complementary 0- O 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 unrelated Books O étv 21 MacBook Air DII 80 F10 F11 F7 FB F9 F6 F4 F5 F3 F1 F2 * @ # $ 7 8 9 1 2 4 P T Y Q W J K S F く Z C V command oF option command O 回 .. - つエ B ** A.
Jason has the following utility function: U = F2C where F is food and C is clothing. Clothing is measured on the vertical axis while food is measured on the horizontal one. Suppose the price of food is €3 per unit, the price of clothing is €2 per unit and that Jason’s income is €36. Calculate the number of units of clothing that Jason consumes in equilibrium. Mary has a different utility function than Jason in Question 2 but faces the same prices as him. Suppose she also only consumes food and clothing but we do not know her utility function or her income. What is Mary’s marginal rate of substitution of food for clothing when her utility is maximized? Explain your answer briefly.
(a) A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good she prefers more to less, with diminishing MRS) chooses optimally to consume 12 units of X. If the prices change and now pX = 6 and pY = 4, what is the possible range for her new optimal X consumption? (b) Forget about (a). A consumer with I=$240 budget is shopping for apples (x) and oranges (y). Apples cost $1 each up until 60 units; thereafter each apple costs $2. Similarly, oranges cost $1 each up until 60 units, and thereafter $2 each. Draw the graph of feasible set of bundles for the consumer with relevant points and numbers (shade the feasible area), no explanation needed. (c)(HARD!) In (b), calculate the optimal bundle assuming the consumer’s utility function is u(x,y) = x5y.

Recommended textbooks for you

ENGR.ECONOMIC ANALYSIS

Economics

ISBN:

9780190931919

Author:

NEWNAN

Publisher:

Oxford University Press

Principles of Economics (12th Edition)

Economics

ISBN:

9780134078779

Author:

Karl E. Case, Ray C. Fair, Sharon E. Oster

Publisher:

PEARSON

Engineering Economy (17th Edition)

Economics

ISBN:

9780134870069

Author:

William G. Sullivan, Elin M. Wicks, C. Patrick Koelling

Publisher:

PEARSON

ENGR.ECONOMIC ANALYSIS

Economics

ISBN:

9780190931919

Author:

NEWNAN

Publisher:

Oxford University Press

Principles of Economics (12th Edition)

Economics

ISBN:

9780134078779

Author:

Karl E. Case, Ray C. Fair, Sharon E. Oster

Publisher:

PEARSON

Engineering Economy (17th Edition)

Economics

ISBN:

9780134870069

Author:

William G. Sullivan, Elin M. Wicks, C. Patrick Koelling

Publisher:

PEARSON

Principles of Economics (MindTap Course List)

Economics

ISBN:

9781305585126

Author:

N. Gregory Mankiw

Publisher:

Cengage Learning

Managerial Economics: A Problem Solving Approach

Economics

ISBN:

9781337106665

Author:

Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:

Cengage Learning

Managerial Economics & Business Strategy (Mcgraw-…

Economics

ISBN:

9781259290619

Author:

Michael Baye, Jeff Prince

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS