3. Suppose the individual has a utility function In(c) where c is consumption and In(·)is the natural logarithm function (that is, logarithm with base e; which is a verypopular utility function used in both economics and finance research). Calculatethe expected utility from each lottery.4. For this specific example, which lottery offers higher value (in terms of expectedutility) and what is it about the shape of the utility function that yields this result? Consider two lotteries. Lottery A is such that an individual receives a prize of 1.25units of a consumption good with 50% probability and 0.75 units of the consumptiongood with 50% probability. Lottery B presents the winner with a prize of 1.5 units ofa consumption good with 50% probability and a prize of 0.5 units of the consumptiongood with 50% probability.

Lottery A: Prize = 1.25 units with probability 0.5 Prize = 0.75 units with probability 0.5 Lottery…

3. Suppose the individual has a utility function In(c) where c is consumption and In(-) is the natural logarithm function (that is, logarithm with base e; which is a very popular utility function used in both economics and finance research). Calculate the expected utility from each lottery. 4. For this specific example, which lottery offers higher value (in terms of expected

3. Suppose the individual has a utility function In(c) where c is consumption and In(-) is the natural logarithm function (that is, logarithm with base e; which is a very popular utility function used in both economics and finance research). Calculate the expected utility from each lottery. 4. For this specific example, which lottery offers higher value (in terms of expected

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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2. Suppose Jill derives utility from not only consuming goods, but also from enjoying leisure time. Let her utility function be defined as follows: U=C.25.R.75 where C is a consumption good that can be bought at a price of $1 and R is hours of leisure (relaxation) consumed per day. There are 24 hours in a day and leisure is defined as time spent not working. Jill has a job that pays $w per hour, a trust fund that pays her $M per day, and she can work any number of hours per day, L, she desires. C, consumption good; R, Leisure (relaxation); L, labor M, non-wage income; w, wage rate. a. Derive her labor supply function? b. Assume M = $100, at what wage is her quantity supplied of hours = 0?
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?
Consider the following money lotteries: ?1=(5/6,3000;1/6,500) ?2=(2/3,3000;1/3,500) ?3=(1/4,3000;1/4,2000;1/4,1000;1/4,500) ?4=(1/2,2000;1/2,1000) Leslie says that she is indifferent between lottery ?1 and getting $2000 for sure is indifferent between lottery ?2 and getting $1000 for sure prefers lottery ?3 over lottery ?4 Explain carefully whether or not Leslie is rational according to the theory of expected utility.
6. If intertemporal preferences are consistent and the lifetime utility function is additive, then the discount function 8(t) must be (a) bounded (b) exponential (c) hyperbolic (d) linear (e) logarithmic
Economics Consider two friends Anna and Elsa whose gains and losses are listed as follows: Anna's investment is worth $2.5 million (decreased from $3.5 to $2.5 million) Elsa's investment is worth $2.2 million (increased from $2 to $2.2 million) For each of them write down the reference utility function (First determine the reference point (use a parameter) and derive reference utility function for each).
2. Suppose there are n identical consumers, each with a utility function u(x, y): = ax = x²+y. Each consumer has different disposable income w. The price of good x is p dollars, and the price of composite good y is equal to 1 dollar. Assume a > 0 and b > 0. (Hint: Question 1) (a) Calculate the marginal utility of good x and good y. Then, calculate the marginal rate of substitution between good x and good y. (b) Calculate the individual demand of consumer 1 for good x. (c) Calculate the aggregate demand for good x. (d) Draw a graph showing the market demand curve for good x. (e) Discuss whether an increase in disposable income for each consumer lead to an increase in the consumption of good x? This increase in disposable income can result from various factors, such as a decrease in taxes, government stipends, or other forms of income support. (f) Discuss the effect on demand for good x if there is an increase in the price of good x. This increase in the price of good x can result from…
Suppose Katie buys the bundle (20,9) from the budget line 3x_1 + 5x_2 = 105. When the price of good 1 changes to p1 = 6 and the price of good 2 remains the same, she buys the bundle (5,15). On a later date when p1 = 5 and p2 = 4, by observing Katie’s choices we can say that the Weak Axiom of Revealed Preference (WARP) is violated if a) She buys the bundle (10,15). b) She buys the bundle (15,10) c) She buys the bundle (23,6) d) She buys the bundle (25,25). e) None of the above choices violates WARP.
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