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- Consider the following utility function for goods x1 and x2: u(x1,x2)=(x1+x2)2 What type of preferences does this utility function represent and why?Donald likes fishing (X1) and hanging out in his hammock (X2). His utility function for these two activities is u(x1, x2) = 3X12X24. (A) Calculate MU1, the marginal utility of fishing. (B) Calculate MU2, the marginal utility of hanging out in his hammock. (C) Calculate MRS, the rate at which he is willing to substitute hanging out in his hammock for fishing. (D)Last week, Donald fished 2 hours a day, and hung out in his hammock 4 hours a day. Using your formula for MRS from (c) find his MRS last week. (E) This week, Donald is fishing eight hours a day, and hanging out in his ham mock two hours a day. Calculate his MRS this week. Has his MRS increased or decreased? Explain why? (F) Is Donald happier or sadder this week compared to last week? Explain.Consider the following utility functions. G(x,y) = x² (1+y) H(x,y) =In(x) + In(2y) +20 L(x,y) = (x+1)1/2 + (y+1) 1/2 U(x,y) = ex+y W(x,y) = 30 x - 4x² + 4 y Z(x,y) = x¹/2 y Which function or functions are homothetic?
- uestion1:Donna and Jim are two consumers purchasing strawberries and chocolates. Jim’s utility function is U (x, y) = xy and Donna’s utility function is U (x, y) = x2y where x denotes strawberries and y denoteschocolates. 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, and Donna’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? What is the optimal bundle for Jim, and for Donna, when the price of strawberries rises to $3?Question2:Consider a one-period ecoI am unsure the direction the utility functions would go in , with this specific scenarioFor the utility function U = Qx0.22Qy(1-0.22) find the trade-off rate between good X and good Y at Qx= 9 and Qy=19 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
- Given a Utility function: U(x,y) = 3xy. Suppose the Price of x is 2, and the price of y is 4. What is the optimal choice of y as a function of x. ( MRS = (Px/Py).You were presented with a utility maximizing rule which states: If you always choose the item with the greatest marginal utility per dollar spent, when your budget is exhausted, the utility maximizing choice should occur where the marginal utility per dollar spent is the same for both goods. That rule is expressed as follows: Group of answer choices (The marginal utility associated with good 1 / the price of good 2) = (the marginal utility associated with good 2 / the price of good 1) % change in price / % change in quantity (The marginal utility associated with good 1 / the price of good 1) = (the marginal utility associated with good 2 / the price of good 2) The marginal utility per dollar of good 1 > the marginal utility per dollar of good 2.Happy Goluki likes tea (good 1) and cookies (good 2). Her preferences are represented by the utility function U(q₁,92) = (q₁)⁰.5+(q₂)0.5, where q₁ is the number of cups of tea and q2 is the number of cookies. Goluki is given I = $180, which she is allowed to spend as she wishes on tea and cookies. a) Calculate Goluki's optimal bundle if the price of tea is p₁=$1 and the price of cookies is p2=$2. Call this bundle A and show it on a graph (put tea on the horizontal axis). b) Suppose that the price of tea increases to $5 (I know, I can't believe it either, but Melbourne does have some very fancy tea places) and the price of cookies stays the same. Calculate Goluki's new optimal bundle of tea and cookies (call it bundle B). Show it on a graph from part a). c) If at new prices (pnew-$5 and p2=$2) Goluki has just enough income to achieve the same utility as in part (a), what bundle will she buy? Calculate this new bundle D and show it on the graph from part a). Calculate the income required…
