find the total utility given the maximum umbination of good x and y. Use. Lagraangian approach. w given: utility function: V = √x + √y budget constraint: 400 = 10x + 20 y
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- Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30Boyd has the following utility function: U= 100B /C where B represents books and C represents audio CDs Boyd currently consumes 46 units of good B and 36 units of good C. His total level of utility is (Enter a numeric response using a real number rounded to two decimal places.) 15 MacBook Air 80 esc F1 F2 F3 F4 F5 F6 F7 @ #3 $ % 1 2 3 4 7 8. Q W E Y tab S caps lock C V * 00 つ エ B LL D A.2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2Y/X and MUy = 2\X/Y ) a) Suppose Y=3. Calculate John's utility for X=4,9,16, and 25. For a given level of Y, does good X display diminishing marginal utility?
- he Calculus of Utility Maximization and Expenditure Minimization -End of Appendix Problem uppose that there are two goods, X and Y. The price of X is $2 per unit, and the price of Y is $1 per unit. There are two onsumers, A and B. The utility functions for the consumers are UA(X,Y)= X05.05 UB(X,Y)= X0.8y0.2 Consumer A has an income of $100, and Consumer B has an income of $300. Using Lagrangians, solve for the optimal bundles of goods X and Y for both consumers A and B. a. The optimal bundle for consumer A is X = 25 and Y* = 50 - b. The optimal bundle for consumer B is X = 120 and Y* = 60If Utility =.5lnX++3Z+10+4√W then Marginal utility from W is...todd is a cattle rancher in june and july he spent his clothing budget on jeans and cowboy hats. each pair of jeans cost $56 and each hat cost $41. At Todd's optimal choice, his marginal utility from the last pair of jeans purchased is 592. This means that his marginal utility from the last cowboy hat purchased is: Round the final answer to the whole number
- Suppose Susan has to choose between purchasing high-definition televisions and milk. Which of the following is the utility-maximizing rule that Susan should follow while choosing the optimal quantities of these two goods? (Note: In the answer options that follow, MU stands for "marginal utility.") O MU of Milk = MU of HDTVS O (MU of Milk) × (Price of Milk) = (MU of HDTVS) × (Price of HDTVS) MU of Milk MU of HDTVS Price of HDTVS Price of Milk MU of Milk MU of HDTVS Price of Milk Price of HDTVS Since milk costs little and high-definition televisions are expensive, it must follow that when people choose their optimal quantities of milk and high- definition televisions to purchase, the marginal utility they receive from the last high-definition television they buy is v than the marginal utility they receive from the last gallon of milk they buy.Denver Bluff High School has $60,000 to spend on computers and other goods so its budget equation is C + X = 60,000, there Cis expenditure on computers and Xis expenditure on other things. The high school's preferences can be represented by the utility function U(C, x) = cx?, where the marginal rate of substitution is -X/2C. Currently, the high school's optimal bundle is $20,000 of computers, and $40,000 of everything else. a. Graph the school's budget line, with computers on the x-axis and all other goods on the y-axis. Label intercepts and the current optimal bundle and sketch an indifference curve. The State Education Commission wants to encourage "computer literacy" in schools, and so has proposed the following plan: Provide the schools with a "matching grant," in which the state will cover $0.50 of every $1 the school spends on computers (effectively lowering the price of 1 unit of C to $0.50). b. If the state adopts the plan, write the equation for Denver Bluff High's budget…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…