Suppose a consumer has preferences described by the utility function u(x1,x2)=a In(x1)+(1-a) In(x2), where In(x) is the natural logarithm of x. For which combinations of parameter a and income m this consumer will spend the lowest amount of money on good 1? Выберите один ответ: O a. a 1/2, m=100 O b. a=1/5, m=200 Oca=1/9, m=500 O d. a=3/4, m=80 O e. a 5/6, m=60
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- Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.Huang is determining how much Coke and Pepsi he will buy. Use the information in italics to answer the bolded question below. • Huang's preferences for Coke (C) and Pepsi (P) are represented by the following utility function: U = 2C + 3P • Huang has $12 to spend on soft drinks. • The price of Coke (P) is $0.50/can. • The price of Pepsi (Pp) is $1.00/can. Which of the following statements referring to Huang's preferences is incorrect. O Huang does NOT experience diminishing MRS. If Huang gives up two cans of Pepsi, he needs to purchase 3 cans of Coke to remain equally satisfied. Pepsi and Coke are perfect substitutes for Huang O None of the above statements are incorrect.Anne is going to the grocery store to buy some fruit. She can buy either apples or oranges. Let a be the quantity of apples she buys, and let zo be the quantity of oranges she buys. Her utility function is: u(xa, xo) = ln xa + 3 ln xo Anne has y pounds to spend. The price of apples is pa and the price of oranges is po (a) (b) Write down Anne's budget constraint and utility maximization problem, and the Lagrangian associated with this utility maximization problem. Find Anne's Marshallian demand functions for apples and oranges. Find Anne's indirect utility function.
- Anthony seeks to maximize the following utility function u(x, y) = x'/3y2/3 subject to the budget constraint Pæa + PyY = I 1 where pr, Py, x, y, I > 0. a) Find Anthony's utility-maximizing bundle (x*, y*) as a function of pæ, Py, and I. b) Show that y* is decreasing in py and increasing in I (hint: use partial derivatives). c) What share of Anthony's income is spent on x? What share is spent on y? In other words, calculate Pa and Pu. Are these shares a function of prices? Pyy* Note: The above utility function is Cobb-Douglas, and all Cobb-Douglas functions have these share formulas for any values for the exponents. d) What is the impact of a change in pr on Anthony's utility?A consumer's utility function is given by u (r_y) := r'/2y}/2 for any nonnegative x and y, representing the consumption quantities of goods x and y, respectively. Suppose that the price of good y is constantly ¢1, and that the consumer is given income m cedis (and nothing else). Denote p, for the price of good r. Based on the quantity demand (p, m) for good r. a. Given that p, > 1/(4m), calculate i (Pz, m) and (Pz, Py, m), then use the Slutsky equation to deduce what the substitution effect r° (pz, y) is equal to. b. Given that p, < 1/(4m), calculate i (P, m) and i (P2, Py, m), then use the Slutsky equation to deduce what the substitution effect r° (Pz; y) is equal to. c. What is your interpretation of the your result in a and b above?Utility maximization with a budget constraint. A hypothetical consumer spends all tgheir income on ramen noodles (N) and wild rice (W). N is the quantity of noodles; W is the quantity of wild rice. Their income is $1,600 per month. the price of noodles is $2 per package and the price of wild rice is $20 per pound. The utility function is U=sqrt(N*W). the MRS = -N/W. The budget constraint is: 1,600 = 2*N + 20*W Graph Qty of noodles (N) on vertical axis and Qty of wild rice (W) on horizontal axis. SOLVE: a. Graph the budget constraint. label all points. What is the slope of the budget constraint? b. Find the optimal quantities of noodles(# of packages) and the wild rice (# of pounds) given the budget constraint. graph these optimal quantities. draw your indifference curve on the same graph. c. Show on your graph what happens when the price of wild rice increases to $40 per pound. Find your new optimal quantities of noodles and wild rice. label all points on graph. label the…Consider a consumer with M = $120 to spend (income) and faces prices PX = $15 and PY =$5 for goods X and Y. Her utility function is U(X, Y) = X1/2 + Y1/2.a Carefully. express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the other…Suppose the utility function for a consumer is given by U = X + Y, where X and Y are a consumer's consumption of goods X and Y. Which of the following bundles does this consumer find indifferent between 10 units of X and 5 units of Y? You Answered a. 4 units of X, 10 units of Y b. 2 units of X, 13 units of Y c. 5 units of X, 7 units of Y d. 8 units of X, 8 units of YAndy purchases only two goods, apples (a) and kumquats (k). He has an income of $1,000 and can buy apples at $10 per pound and kumquats at $10 per pounc utility function is U(a, k) = 4a + 3k. What is his marginal utility for apples and his marginal utility for kumquats? Andy's marginal utility for apples (MU) is MU, = and his marginal utility for kumquats (MU) is MU, = (Enter your responses as whole numbers.) What bundle of apples and kumquats should he purchase to maximize his utility? Andy should consume apples and kumquats. (Enter your responses as whole numbers.) React tv MacBook Air 80 DI DD F1 F2 F3 F5 F6 F7 F8 F9 F10 @ #3 $ % & 1 2 4 7 8. 9 Q W E Y { A S F G H. J C V M ption command command option .. .. V B