Skippy has the utility function u = budget constraint B = pxx + PyY. x²y and the (a) Find the optimal x and y and verify that Skippy's utility is maximized.
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- Find utility functions given each of the following indifferencecurves [defined by U()=k ]: a. z=k1/x/y/ b. y=0.5x24(x2k)0.5x c. z=y44x(x2yk)2xy22xU(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.Q- Marginal utility can never be negative. True/False
- Charlie's utility function is (1-a) U(xa, XB) = Ax“xr-) where A > 0 and a > 0Donald 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.Question 1 Consider a consumer with utility x₁2/3x21/3 and a budget constraint of 3x₁+6x2 ≤100. What is the maximum utility the consumer can achieve
- 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 30Suppose a consumer consumes two goods, x and y and has utility function U(x, y) = min{3x, 2y}. She has a budget of $100. The price of x is $35 and the price of y is $10. a. If x is on the horizontal axis and y is on the vertical axis. Please find the consumer's MRS. b. Find the consumers 's optimal choice of x and y..Suppose a consumer has the following different utility functions, derive the marginal utility of X and Y for each utility function (a-c) AND determine if the Law of Diminishing Marginal Utility applies. a. U = 4x²y
- Consider a consumer with the utility function u(x1,x2) = x11/3 x22/3. a. Find the Marginal Utility for each good. b. Find the slope of one of this consumer's indifference curves c. Write down the consumer's budget constraint. d. What is the slope of this consumer's budget constraint? Show how you derived your answerLionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.
