2. An individual has an intertemporal utility function that is rational,monotonic, and strictly convex. She can borrow/lend at the interest rate, r,but does not have access to human capital. She is currently consuming abundle such that MRSx₁x2 >1+r. How many of the following statementsCOULD BE true? [HINT: try drawing a picture]0X1x2The bundle is optimal (i.e. maximizes her utility).If the individual is consuming both goods, she could do betterby consuming less today and consuming more tomorrow.She is at a corner solution in which she only consumestomorrow.a. 1b. 2c.3V.d. None of the above statements could be true.

The intertemporal utility function means the consumption is distributed between present and future.…

An individual has an intertemporal utility functi monotonic, and strictly convex. She can borrow/lend at the interest rate, r, but does not have access to human capital. She is currently consuming a bundle such that MRS×₁x2 >1+r. How many of the following statements COULD BE true? [HINT: try drawing a picture] 0 0 0 The bundle is optimal (i.e. maximizes her utility). X If the individual is consuming both goods, she could do better by consuming less today and consuming more tomorrow. She is at a corner solution in which she only consumes tomorrow.

An individual has an intertemporal utility functi monotonic, and strictly convex. She can borrow/lend at the interest rate, r, but does not have access to human capital. She is currently consuming a bundle such that MRS×₁x2 >1+r. How many of the following statements COULD BE true? [HINT: try drawing a picture] 0 0 0 The bundle is optimal (i.e. maximizes her utility). X If the individual is consuming both goods, she could do better by consuming less today and consuming more tomorrow. She is at a corner solution in which she only consumes tomorrow.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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3. Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 5A/4B³/4. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method. b. Suppose Pa increase. Show graphically the income, substitution effect and total effect and explain. c. Suppose PA increase. Show the graph for CV and EV and explain.
Jien is just bored all the time; no amount of success makes him happy, it seems. Below is a list of his income for the last several years and the utility he experienced per dollar of income: Year Yearly Income Utility per Dollar Earned 2017 $60,000 2 utils 2018 $70,000 1.8 2019 $100,000 1.5 2020 $120,000 1 2021 $145,000 0.40 From the above, we can say that Jien most likely is different from most people economists study in terms of risk attitudes is "risk loving" will not take a fair bet has a utility of wealth curve that is a straight line
3rian earns income equal to $82,000 in the first period, but his income will drop to $19,170 in the second period. a Sketch his intertemporal budget constraint, ansuming a 6.5% interest rate. Add an indifference curve that assumes he optimally chooses to save $40,000 in the first period. Be sure to CLEARLY graph your answer, with labeln on the axes and any other important points. Also show work for any calculations done. b. Show the offect of a 50% tax on interest income, assuming the substitution and income effects cancel each other out. Again, be sure to clearly graph your answer and show work for any calculations done.
a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?
Pls help with thsi question I am stuck Given the image attatched: 1.Given the above Marginal Utilities and prices to form the optimality condition for utilitymaximization. According to this optimality condition, what must be the ratio of Films toBooks in an optimal consumption bundle? 2. Given your answer to Q9, what must be the household’s optimal consumption of F & Bgiven their income (m)? 3. Suppose that the price of Films changed from $2 to $4. What would need to happen tothe MRS according to the optimality condition in Q9 if the household wanted to keepmaximizing its utility?
Columns 1 through 4 in the following table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are, respectively, $18, $6, $4, and $24 and that Ricardo has an income of $106. a. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule.
Brian earns income equal to $82,000 in the first period, but his income will drop to $19,170 in the second period. a. Sketch his intertemporal budget constraint, assuming a 6.5% interest rate. Add an indifference curve that assumes he optimally chooses to save $40,000 in the first period. Be sure to CLEARLY graph your answer, with labels on the axes and any other important points. Also show work for any calculations done. b. Show the effect of a 50% tax on interest income, assuming the substitution and income effects cancel each other out. Again, be sure to clearly graph your answer and show work for any calculations done.
2. Ann has started working and is saving to buy a house, which requires a down-payment of d. She has a monthly income of y and faces goods prices pa and p3. Ann's utility function is given by u = 3 In a. + (1- 3) In a. %3D Her minimum standard of living renders a utility of uo. Solve for the minimum number of months it takes for Ann to save up to the down-payment, as a function of (d, y, uo, Pa, Ps).
3. Suppose Mary enjoys Pepsi and Coke according to the functionU(P;C) = 4C + 5P. What does her utility function say about her MRS of Coke for Pepsi? What do her indi§erence curves look like? What type of goods are Pepsi and Coke for Mary? If Pepsi and Coke each cost $1 and Mary has $20 to spend on these products, how many units of each product should she buy in order to maximize her utility? Show this utility maximiz- ing combination combination of Pepsi and Coke on the graph. how would her consumption and utility maximizing bundle of Coke and Pepsi change if the price of Coke decreases to 50 cents. 4. Vera is an impoverished graduate student who has only $100 a month to spend on food. She has read in a government publication that she can assure an adequate diet by eating only peanut butter and carrots in the Öxed ratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides to limit her diet to that regime. a) If peanut butter costs $4 per pound and carrots cost $2 per…
Columns 1 through 4 of the accompanying table show the marginal utility, measured in utils, that Ricardo would get by purchasing various amounts of products A, B, C, and D. Column 5 shows the marginal utility Ricardo gets from saving. Assume that the prices of A, B, C, and D are $18, $6, $4, and $24, respectively, and that Ricardo has an income of $105. Column 1 Column 2 Column 3 Column 4 Units Units Units Units of A MU of B MU of C MU of D MU 1 72 1 24 1 15 1 36 54 15 12 2 30 3 45 3 12 3 8. 3 24 4 36 4 7 4 18 27 7 5 5 13 6 18 6 5 6 4 6 7 7 15 7 2 7 3.5 7 8 12 8 1 8 3 8 2 а. What quantities of A, B, C, and D will Ricardo purchase in maximizing his utility? b. How many dollars will Ricardo choose to save? c. Check your answers by substituting them into the algebraic statement of the utility-maximizing rule. In other words, show it works when using this rule.
b ) Suppose a household is faced with the choice between consuming gasoline ( G ) and all other goods ( OG ) . Today the household consumes 800 liter of gasoline a year. Suppose then that a gasoline price increase is perfectly compensated by a wage increase . If the family followed the utility maximization model , how would this affecti their consumption of gasoline ? Explain by using a figure .
Problem Set 1. A firm's production function is º=50L-0.01Ľ' , where L denotes the size of the workforce. Find the value of MP in the case when: (a) L=1, (b) L=10, (c) L=100, (d) L=1000 Does the law of diminishing marginal productivity apply to this particular function? 2. Show that the price elasticity of demand is constant for demand functions of the form A P = Q" where A and n are positive constants. 3. The demand and total cost functions of a good are respectively 4P+Q-16=0 and ТС %3D 4 + 20 — 10 20 a) Find expressions for TR, (profit) 1 , MR, and MC in terms of Q. b) Solve the equation dn = 0 ÕP and hence determine the value of Q which maximizes profit. c) Verify that, at the point of maximum profit, MR=MC. 4. The cost of building an office complex, x floors high, in a prime location in Accra is made up of three components: (a) GH¢10 million for the land (b) GH¢'/, million per floor (e) Specialized costs of GH¢10000× per floor. How many floors should the office complex contain if…