3 5. Given the following utility functionU (c1, C2) = [ac{ + (1 – a)c²]/?where 0 < a,p < 1.a. Find U and U, and explain their intuitive (economic) meaning.C1b. Find Uc, to determine how U, varies with c2 (increase/decrease as c2 increases).What is the intuitive (economic) meaning of how U, varies with c2?c. What does the level curve U(c1, c2) = U, represent?d. Find the marginal rate of substitution of c1 for c2 at a point on the level curveU(c1, c2) = Ug.e. Find the elasticity of substitution between c, and c2.

As the bartleby rules we are allowed to answer only the 1st three parts of any question when it has…

5. Given the following utility function U(c1, c2) = [ac{ + (1 – a)c²]? where 0 < a, p < 1. a. Find U, and U, and explain their intuitive (economic) meaning. b. Find Uc, to determine how Uc, varies with c2 (increase/decrease as c2 increases). C1C2 What is the intuitive (economic) meaning of how U varies with c2? c. What does the level curve U(c1, c2) = U, represent?

5. Given the following utility function U(c1, c2) = [ac{ + (1 – a)c²]? where 0 < a, p < 1. a. Find U, and U, and explain their intuitive (economic) meaning. b. Find Uc, to determine how Uc, varies with c2 (increase/decrease as c2 increases). C1C2 What is the intuitive (economic) meaning of how U varies with c2? c. What does the level curve U(c1, c2) = U, represent?

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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suppose that a consumer has a utility function U(x,y) = x1/3 y2/3 At the point (x,y) = (4,7) in order to keep utility the same and get one more unit of x, the consumer would be willing to give up how many units of y ? (a) 7/4 (b) 4/7 (c) 7/8 (d) 4/14
2. Tom spends all his $100 weekly income on two goods, apples and bananas. His utility function is given by U (A, B) = AB, where A and B stand for the quantity of apples and bananas consumed by Tom. If PA = $4 and PB= $10, how many apples and bananas will he consume? Make sure you write out the utility maximization problem explicitly, including the decision variable(s). What if his utility function is given by U (A, B) = A0.5B 0.5?
1) Suppose that a person consumes two goods, x and y, in fixed proportions. He or she always consumes 1 unit of x together with 3 units of y no matter what the relative prices are.a) What is the mathematical form for this person's utility function?b) Calculate the Marshallian demand functions for both goods for this person.c) Calculate the indirect utility function and the expenditure function for this person.d) In class we discussed why expenditure functions are concave in prices. Is the expenditure function you calculated in part (c) concave in ???
4. Suppose a person has $8 to spend only on apples and bananas. Apples 1 cost $0:4 each, and bananas cost $0:1 each. Furthermore, his preferences for apples (A) and bananas (B) can be represented by U = pAB. a) If A = 5 and B = 80, what will utility be?b) If A = 10, what value of for B will provide the same utility in part a? c) If A = 20, what value of for B will provide the same utility in parts a and b?d) Graph the indi§erence curve implied by parts a through c.e) Give the budget constraint, which of the points identiÖed in parts a through c can be bought by this person?f) show through some examples that every other way of allocating income provides less utility than does the point identiÖed in part b. graph this utility maximizing situation.
Mats, who has reference-dependent preferences over beer and money, goes to the local pub with a friend, but is not planning on drinking any beer or spending any of his 50 Euro in cash. Let his end-of-evening outcomes in pints of beer consumed and cash be c1 and c2, respectively, and let his reference point in pints of beer and cash be r1 and r2, respectively. Then, Mats’ utility is given by v(6c1 − 6r1) + v(c2 − r2), where v(x) = x for x ≥ 0, and v(x) = 1.5x for x < 0. (a) Suppose that the price of beer is pB. Calculate Mats’ utility from drinking one pint of beer at this price. What is Mats’ utility from drinking no beer? And, comparing these two utility values, what is the maximum price pB that Mats would pay for one beer? (b) Suppose that Mats unexpectedly gets a pint of beer as part of a promotion at the pub, and incorporates its consumption into his reference point in beer. [Hint: this means that (r1, r2) = (1, 50).] Suppose that Mats could sell the beer at a price pS.…
Answer the question on the basis of the following two schedules, which show the amounts of additional satisfaction (marginal utility) that a consumer would get from successive quantities of products J and K. Units of J MUj Units of K MUk 1 56 1 32 2 48 2 28 3 32 3 24 4 24 4 20 5 20 5 12 6 16 6 10 7 12 7 8 What level of total utility is realized from the equilibrium combination of J and K, if the consumer has a money income of $28 and the prices of J and K are $8 and $4, respectively? Multiple Choice a. 172 utils b. 168 utils c. 188 utils d. 72 utils Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
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3. Suppose that Omar’s marginal utility for cups of coffee is constant at 1.5 utils per cup, no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is 10 for the first doughnut he eats, 9 for the second he eats, 8 for the third he eats, and so on (that is, declining by 1 util per additional doughnut). In addition, suppose that coffee costs $1 per cup, doughnuts cost $1 each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. How big would that budget have to be before he would spend a dollar buying a first cup of coffee? *use tables and/or graphs if possible, please original work
J 4 True or false? Be sure to explain your answer in detail. Suppose the utility function u(x1, x2) = 2x1x2 represents a consumer's preferences. Then the utility function v(x1,x2) = x1x2 also represents the same consumer's preferences
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True or false with reasoning: 1) _______When we claim that utility can be ordinally measured, we assume that the consumer is able to measure the total and marginal utility received when one extra unit of a commodity is consumed. 2)_______If MRS between two goods is constant, then having more of one good without having more of the other does not increase utility. 3)_______Marginal Utility increases until total utility is at a maximum and then marginal utility decreases.
The utility derived by a consumer from the consumption of two commodities is given by the function U (A, B) = 0.5In (A) + 0.5 In (B) where A are the number of units of the first commodity consumed and B are the number of units of the second commodity consumed each month. A unit of the first commodity costs $8 and a unit of the second commodity costs $ 4 using the Lagrange multiplier method determine the optimal quantity of each of the commodities consumed each month given that consumer has $32 to spend on both commodities each month