The utility function is: I In(C2) U = In(C1) + 1+P The budget constraint is: -C2 =Y1+ T+r 1 Y2 C1 + 1+r 1. Find the utility maximizing values for C, and C2
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- A 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).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 <= 50You 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
- The goal of the consumer is to maximize the total utility or satisfaction derived from their purchase choices, given the unique budget constraint. To calculate total utility of a given combination of T-shirts and movies, one would use the following approach: Group of answer choices For a given combination of T-shirts and movies, assign a number of utils to that combination. For a given combination of T-shirts and movies, survey a group of individuals to determine an average for utils to be assigned to the number of T-shirts and movies. Use utils as a measure of utility, assigning a specific number to T-shirts and movies, and then add those together. For a given combination of T-shirts and movies, use Google to identify the number of utils associated with the number of T-shirts and movies and then sum them.Assume a consumer with the utility function U = U (X, Y) = X2 Y2 and the typical budget constraint M = PxX + PyY a. Set up the constrained maximization problem and derive the first-order conditions. b. Derive the consumer’s demand for X and Y in terms of the parameters.why is there no inclusion of the parameter z in the solutions and the budget constraint?
- 1. Use budget constraints to express consumption levels, ct and ct+1. (Hint: Use income conditions given above in the budget constraint. Notice that there are two possible states in the second period.)2. Rewrite the utility maximization problem as choosing the optimal at alone. (Hint: Replace ct and ct+1 in the utility function with your answers from point 1. Use probabilities to derive the expected value in the utility function. Remember that a random variable that takes values x1 in state one with probability p and x2 in state two with probability 1 − p has the expected value E [x] = p.x1 + (1 − p).x2)3. Derive the first order condition and find the optimal value of savings, at. (Hint: The only control (choice) variable is at)4. Does household accumulate precautionary savings to self-insure against the scenario of low income in the second period? Why or why not?A young consumer has to decide how to spend his spare time. He can either watch movies x or play online video games y. Each round of the game cost 20 and each movie cost 20. He has 200 dollars to spend each week. In addition, he has time constraint. He can spend no more than 20 hours for entertainment each week. A movie last 2 hours and playing a game takes about 1 hour. His utility is given by √xy. Use the Kuhn-Tucker condition to find his optimal choice. (Assume that x and y can take any value, not necessarily integers.) Does the solution satisfy the necessary and sufficient condition for a maximum?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.
- Albion is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Albion has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function where b =4. The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.what is the derivative of the utility function UU = log (100-2PPii) + log(PPjj+PPdd) with respect to PPjj. Budget constaint XXii = 100 - 2PPiiAssuming, 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 coffee