The utility function is given by u(x,,X2)=5ln(x1)+7ln(x2). For prices p,=2 and P2=4, what is the slope of the Engel curve (for good 2) at point x2=3.9? If your answer is not integer, round it to 2 digits after the decimal point.
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- Marina decides to purchase a ring made from an alloy composed exclusively of gold (G) and titanium (T). The price of gold is $60 per gram, and the price of titanium is $30 per gram. Her total budget for the ring is $600. Her utility function is given by U(G,T) =GT. Suppose the price of titanium falls to $20 per gram. At the final basket, the optimal amount of titanium is（）grams.Suppose the market demand curve for pizza can be expressed as QD = 100 - 2P + 3Pb, where QD is the quantity of pizza demanded, P is the price of a pizza, and Pb is the price of a burrito. What is the slope of this demand function, and what information does the slope provide?..Suppose the function for the utility from good c is denoted as U(c)=2c1/2 . Which of the following expressions indicates the marginal utility of c?
- . Ceja has utility function U=A2*B2 , where A equals the number of apples she eats each week, while B is the number of bananas she eats each week. Ceja has $20 to spend on fruit each week. The price of an apple is $1, while the price of a banana is $0.25. Find out the combination of Apples and Bananas that maximize Ceja’ satisfactionA consumer's preferences are represented by the utility function If the budget constraint is P1X1 + P2X2 = M, determine the demand functions q1(P1, P2, M) and Q2(P1, P2, M). Determine also the indirect utility function V(P1,P2,M).Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F) = 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $4000. Suppose F is on the horizontal axis and D is on the vertical axis. Jane's marginal rate of substitution between F and D is equal to 10 1 F/D D/F
- Assume a consumer has a utility function U(x1, x2) = x1x2 where x1, x2 represents the amount of two goods 1 and 2 consumed in a given time period, find the utility-maximizing consumption function subject to the budget constraint5x1 + 4x2 <= 50If the utility function for a consumer is defined by U=f(X,Y)=3√(X^2Y), Given that the consumer's income is 900 currency units and unit price of goods X and Y are 20 and 30 currency units respectively, find the combination of X and Y which optimize the consumer satisfaction.You have k20 per week to spend and two possible uses for the money: telephoning friends back home and drinking coffee. Each Hour of phoning costs k2 and each cup of coffee costs k1. Your utility function is U(X,Y)=XY,where X is the hours of phoning you do and Y the number of cups of coffee you drink. What are your optimal choices? What is the resulting utility levels? You can use the standard result on the constrained maximization of such a function, but must state in clearly
- Prove that the utility maximization conditions as suggested by the “marginal utility framework” are consistent with the “indifference curves approach”.Assuming, there are two goods: Coffee and Tea. Your budget is 18,000 KRW per day. The price of Coffee ranges between 0 KRW to 6,000 KRW. The price of Tea ranges between 0 and 5,000 KRW Specify your indifference map of your preference relation Specify your utility function Specify a budget constraint based on the assumption above Specify your own-price offer curves for coffee Specify your curve Engel curve for coffeealculate the marginal rate of substitution (MRS12) for the following utility function: U(q1,q2)= 60q1+ 0.2(q2)2 What is the value of MRS12 at bundle (4, 3)?
