Suppose consumer are always ready to trade k units of good X for w units of good Y. Then, which of the following utility function represents this preference? U(X,Y) = min{wX + kY). O U(X,Y) = wX + kY. O U(X,Y) = min{kX, wY}. O U(X,Y) = kX + wY.
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- 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 If the consumer has money income of $52 and the prices of J and K are $8 and $4 respectively, the consumer will maximize her utility by purchasing Multiple Choice 3 units of J and 7 units of K. 5 units of J and 5 units of K. 4 units of J and 5 units of K. 6 units of J and 3 units of K.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 preferencesReese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Suppose that now Reese loses almost his entire income, so that he is left with only one dollar, i.e. his new income is I0 = 1. If prices are still px = 2, py = 4, what is his new optimal consumption of x and y (Hint: Remember that consumption of both goods must be weakly positive, i.e. x∗ ≥ 0 and y∗ ≥ 0) (a) x∗ = 0.5, y∗ = 0(b) x∗ = 0.25, y∗ = 0(c) x∗ = 0.75, y∗ = 0.25(d) x∗ = 0.75, y∗ = 0(e) x∗ = 0.5, y∗ = 1
- Suppose that the utility function U(C, S) = C + 2S^1/3 describes Molly’s preferences over two goods:Carrots (c) and Spinach (s). Give another utility function that represents Molly’s preferences just as well as the one given above. Justify your answer by showing that your new utility function has the same formula for MRS as the given one.Assume an individual's utility from consuming good #1 and good #2 is given by the following function: U (q1 , q2) = min (q1 , 2q2) Suppose the price of good #1 is $1 (p1=1) and the individual's income is $10 (y=10). If this individual's utility maximizing decision is to purchase 2 units of good #2 (q2=2), what must be the price of good #2?Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.
- Meera's budget line relating to good X and good Y has intercepts of 12 units of X and 10 units of Y. If the price of X per unit is 10, Meera's budget on the two goods is Oa. 100 Ob. 120 Oc. 240 O d. 220Suppose you have utility given by U = x^.5y^.5. Px = $1 and Py = $1, m=$12. If the price of y increases to $3, calculate the equivalent and compensating variation. Illustrate the answer graphicallyA consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose that the utility derived by the consumer from x units of Commodity A, and y Commodity B is given by the Cobb-Douglas utility functionU (x, y) = 10x0.6y0.4a. How many units of each commodity should the consumer buy tomaximize utility?b. Is the budget constraint binding?
- You are choosing between two goods, X and Y, and your marginal utility from each is shown in the following table. Units of X MUx Units of Y MUy 1 10 1 8 2 8 2 7 3 6 3 6 4 4 4 5 5 3 5 4 6 2 6 3 a. If your income is $9 and the prices of X and Y are $2 and $1, respectively, what quantities of each will you purchase to maximize utility? ______units of X and ______units of Y b. What total utility will you realize? ______utils c. Assume that, other things remaining unchanged, the price of X falls to $1. What quantities of X and Y will you now purchase? _____units of X and ______units of Y d. Using the two prices and quantities for X, complete the table to derive the demand schedule (a table showing prices and quantities demanded) for X. Instructions: Start with the highest price first Price of X Quantity Demanded of X $ $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 G and H. Units of G MUG Units of H MUH 1 36 1 70 2 33 2 60 3 27 3 55 4 21 4 45 5 18 5 30 6 12 6 25 7 6 7 15 If the consumer has a budget of $29 and the prices of G and H are $3 and $5, respectively, the consumer will maximize their utility by purchasing Multiple Choice 3 units of G and 4 units of H. 4 units of G and 2 units of H. 1 units of G and 5 units of H. 2 units of G and 5 units of H.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.…
