not use ai please A player has $100 today that he needs to consume in the next three periods, t = 1, 2, 3. The utility ofconsuming Sxt in period t is given by the utility function u(x) = In(x), and in period t = 1 the player values his netpresent value of all consumption as u(x1) + \delta u(x2) + \delta 2u(x3), where \delta = 0.9.a. How does the player plan to spend the $100 over the three consumption periods?b. Imagine that the player knows that in period t = 2 he will receive an additional gift of $20. How will he choose toallocate his original $100 initially and how will he spend the additional $20?

Step 1: A budget constraint also demonstrates the quantities of goods and/or services that a…

Answered: A player has $100 today that he needs…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider a consumer who can borrow or lend freely at an interest rate of 100% per period of time (think of the period as being, say, 30 years, a bit like with a mortgage). So r = 1.0, or 100%. The consumer's two-period utility function is: U = In(ct) + (1/2)In(Ct+1) The consumer earn Y=100 each period, so Y₁=100 and Yt+1 also equals 100. If this consumer is behaving optimally, trying to maximize her lifetime utility subject to the IBC, what's her consumption in period t?
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Assume a consumer has current-period income y = 200, future-period income y′ = 150, current and future taxes t = 40 and t′ = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume according to the following utility function: U (c, c′ ) = ln(c) + ln(c′ ). Show mathematically the lifetime budget constraint for this consumer. Find the optimal consumption in the current and future periods and optimal saving. Suppose that instead of r = 0.05 the interest rate is r = 0.1. Repeat parts (a) and (b). Does the substitution effect or the income effect dominate?
V*(p1, p2, 1) = True False P₁ P₂ 1² is a valid indirect utility function.
Mavis earns income in two periods, M, and M2 and buys consumption goods in twd periods as well, C, and C2 (the numbers indicate the period in which the income is earned and the consumption goods are purchased). Her utility function is as follows: U=U(C, ) +: U(C,) where & is the time rate of preference and 1+8 U(C,)=U(C,) when C, = C, and U(C) is well behaved. Mavis can borrow money from or save money at a local bank. The interested rate (whether saving or borrowing) is r. а. Write out Mavis' utility maximizing Lagrangian equation. No need to solve it. b. Describe the process for conducting the comparative statics necessary to determine the sign of the following change: Or С. What is the significance of 6? Assuming you would graph her consumer choice model with C on the horizontal axis, explain why a higher value for & would make her indifference curves steeper or flatter. d. Draw the consumer choice graph for this situation such that M1 = $10,000, M2 = $20,000 and both 8 =0.25 andr =…
of 55 The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume
what is the derivative of the utility function UU = log (100-2PPii) + log(PPjj+PPdd) with respect to PPjj. Budget constaint XXii = 100 - 2PPii
Suppose Jack lives for two periods. Period one is his working life, during which he earns income $50,000; period two is his retirement, during which he earns nothing. During retirement he consumes from the savings during his working life. The rate of interest on his savings is 10%. His consumption during his working life is Cw, and his consumption during his retirement life is Cr. Assume that Jack's utility function is a standard utility function exhibiting diminishing marginal rate of substitution between Cw and Cr. His current consumption during the working life is 75% of his earned income. a. Using the intertemporal choice model, draw a well labeled graph that details all the information discussed above. Notably, indicate the slope of the budget constraint, the intercepts of the budget constraint on both axes, the value of current and future consumptions, and the current savings. Keep in mind that no tax has been imposed on the saver, yet. b. Now the government taxes interest…
Using a diagram, draw the outcome of optimal choice using an indi↵erence curve and the individual’s lifetime budget constraint.
Consider the problem of an individual that has Y dollars to spend on consuming over two periods. Let c denote the amount of consumption that the individual would like to purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase cı units of the consumption good at a price P and can save any unspent wealth. Use sı to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the individual has at his/her disposal to purchase consumption goods in period 2 is (1+r)81. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2. 2 The individual's total happiness is measured by the sum of period utility across time, u(cı) + u(c2). Let u(c)…
Q1. Consider a consumer with a lifetime utility function U(c, c') = u(c) + Bu(c) that satisfies all the standard assumptions listed in the book. The period 1 and 2 budget constraints are c+s=y c+sy+(1+r)s (a) What is the optimal value of s'? Impose this optimal value and derive the life-time budget constraint.
Eren’s two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V^2MLast year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV).

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