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- If marlow obtained 9 units of utility per dollar spent on apples and 6 units of utility per dollar spent on oranges, then Marlowesuppose 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) 4/14Q.3 A utility function is given by the equation U = 120 x0.7 y0.3 where x is the number of hours spent playing golf and y is the hours spent playing cards per month. Calculate the values of x and y for which utility is maximised, subject to the constraint 21x + 3y = 180
- V1 Question I Maximize the following utility function: U=4x 2 +3xy 2 +y 2 ; subject to the condition that x+y=602. 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?6 If someone has an income of 20 and he wants to buy Pepsi and hamburgers. Hamburgers are sold in an unusual way. There is only one supplier and the more hamburgers he buys, the higher the price per unit. So, hamburgers cost is a total of 2h^2 (squared) for hamburgers. Pepsi is sold at a price of $2. 1. In this case, write out the budget constraint of hamburgers and Pepsi. 2. His utility function is u(h,p) = 12h + 4p. Draw his 1) budget line and 2) a few indifference curves on a graph. 3. What is the optimal bundle for him?
- What kind of preferences are represented by a utility function of theform u(x1, x2) = √x1 + x2? What about the utility function v(x1, x2) =13x1 + 13x2?Suppose that at current consumption levels an individual's marginal utility of consuming an extra sandwich is 10 whereas the marginal utility of consuming an extra coffee is 2. Then the MRS (of coffee for sandwiches) that is, the number of sandwiches the individual is willing to give up to get one more coffee is a 5 b. 2 C.1/2 d. 1/5a) The demand and supply functions of a particular good are given by the equations 5pq = 10 5p + 5q +15
- Your sister’s utility function over the 2 goods X and Y is defined by: U (X,Y) = XY +4Y a. If she originally consumed 10 units of X and 24 units of Y, and if the consumption of X were increased to 12 units, how much Y would she be willing to give up and maintain the initial level of satisfaction? That is, how much less Y is needed in exchange for the increase in the consumption of X if she is to be equally satisfied before and after the change occurs? b. On a carefully constructed graph (you only need to consider X and Y values up to 50), indicate your sister’s original consumption position, with X plotted on the horizontal axis and Y on the vertical axis. Draw her indifference curve through the original consumption bundle from part a. As you can verify (or have already verified), she is indifferent to the points (10,24) and (12,21). If you double the amount of each good in these two consumption bundles, you would have the bundles (20,48) and (24,42). Since the two original bundles…A young connoisseur has $600 to spend to build a small wine cellar. She enjoys two vintages in particular: a 2001 French Bordeaux (xf) at $40 per bottle and a less expensive 2005 California varietal wine (xc) priced at $8. If her utility is U(xf, xc) = xf2/3xc1/3, then how much of each wine should she purchase?I have two utility equations U= x^2 + y^2 U = x + ay Please draw the IC curves for each of them. And also, find the cost function associated with them and detailed steps. P.s The cost function for U= x+ay is u.min((p(x),p(y)/a)), but do not know how to get i