The queen of england has utility function u(x,y) =xy and the queen is endowed with basket (x,y) = (4,10). if the queen gives up 3 units of good y, how many additional units of good x does she needs to keep her utility constant? a. 1.71 b. 1.99 c. 2.11 d. 2.24
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- Solve; a consumer utility function is given as 64q10.5q20.25q30.4 1. what is the marginal utility of consuming commodities q1, q2 and q3 2. derive the second-order partial derivatives of the utility function with respect to the three pairs of commodities 3. show the cross partial derivatives with respect to q1 4.what is her total utility when q1 is 24, q2 is 30, and q3 is 15A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 NA 2 82 4 2 26 6 2 60 3.5 3 118 3.6 3 36 5 3 84 3 4 148 3 4 44 4 4 100 2 5 170 2.2 5 50 3 5 110 1.25 6 182 1.2 6 54 2 6 116 0.75 7 182 _0 7 56.4 _1.2 7 120 _0.5_ Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 ___NA__ 2 82 4 2 26 6 2 60 __3.5_ 3 118 3.6 3 36 5 3 84 __3___ 4 148 3 4 44 4 4 100 __2___ 5 170 2.2 5 50 3 5 110 _1.25___ 6 182 1.2 6 54 2 6 116 _0.75__ 7 182 0 7 56.4 1.2 7 120 _0.5_ How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all…
- Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…4. Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows : Kate's net worth is $ 4.5 million ( decreased from $ 5.5 to $ 4.5 million ) Mary's net worth $ 3.2 million ( increased from $ 3 to $ 3.2 million ) ( First determine the reference point ( use a parameter ) and then derive reference utility function for each ) .Assume an individual spends all of the their income on a bundle comprised of good #1 and good #2. In particular, their utility function is given by: U(q1,q2) = q12/3q21/3 Assume the price of good #1 is $1 (p1=1) and the price of good #2 is $3 (p2=3). What must the individual's income be if they maximize their utility by purchasing 10 units of good #1?
- Suppose the consumer's utility function is given by U(x,y) = X3/5y2/5, and the exogenous variables are given by M = 500, Px = 5, and Py = 4. Price of y changes to Py = 2. What is the income effect ony?O A.-14.53O B. +14.53O C. +24.21O D. +25.79O E. None of the above Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.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?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.…
- Bob has a utility function U(x, y) = √x1 + 0.8√x2 + 0.64√x3 over his incomes x1, x2, x3 in the next three years. This function is an example of (A) expected utility; (B) quasi-hyperbolic utility function; (C) discounted utility; (D) none of the above. . Which of the following preferences agree with Bob’s utility? (A) (9, 10, 11) ≻ (9, 10, 12); (B) (9, 10, 11) ≻ (11, 10, 9);(C) (9, 10, 11) ≻ (9, 11, 10); (D) none of the above. Bob’s utility function implies (A) time stationarity; (B) transitivity; (C) impatience; (D) all of the above.1.Suppose that Chris's utility function is given by UC=QC1/2 RC1/2 , where QC and RC are his consumption of Q and R, respectively. Dana's utility function is given by UD=QD1/3 RD2/3, where QD and RD are her consumption of Q and R, respectively. Write an equation for the marginal rate of substitution (MRS) between Q and R for each of the two agents. 2.Suppose that the price of good R is pR=1 and the price of good Q is pQ=2. How much is Chris's and Dana's initial income, given his endowments and given these prices? 3. At these prices, how many units of Q would Chris and Dana want to consume? 4. At these prices, how many units of R would Chris and Dana want to consume?Suppose the consumer's utility function is given by U(x,y) = X3/5y2/5, and the exogenous variables are given by M = 500, Px = 5, and Py = 4. Price of y changes to Py = 2. What is the income effect ony?O A.-14.53O B. +14.53O C. +24.21O D. +25.79O E. None of the above