1. [35 marks]An individual derives utility from consumption spending C and leisurelaccording to the following utility function:U(C,1)=C"1¹-awhere 0>x>1. Leisure time in hours is given by:1=T-Hwhere T is hours of total time available and H is hours of work. The consumer'sreal income is given by:C=w (T-1)+Nwhere w is real wage and N is real non-labour income.a) Derive the optimal values of C, I and the Lagrangian multiplier if the individualwishesmaximise utility subject to thetoconstraint:C=w (T-1)+N.[15 marks]

The objective of this question is to find the optimal values of consumption (C), leisure (l), and…

Answered: 1. [35 marks] An individual derives…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose the real interest rate is 0%. Daniel worked for 60 years and he retired for 20 years. When Daniel had a job, his annual income was $10,000. During retirement, the annual pension he received was $6,000. Suppose Daniel smoothed consumption completely. What was the amount of savings Daniel had when he retired? O $16,000 O $120,000 $600,000 $60,000
4 Assume that a person's utility over two goods is given by U(g1; g2) = g1 + ln g2. The price of good g1 is equal to p1 and the price of good g2 is p2. The total income of the individual is given by I. The marginal rate of substitution between g1 and g2 is given by 1/(1/g2). Then, the expressions for this person's (1) budget constraint, (2) budget line's slope (assume that, graphically, g1 is on the horizontal axis and g2 on the vertical axis), and (3) the person's demand function for g2 (that is, g2 as a function of price ratio) are respectively:
26. Given this diagram; what is the equilibrium level of income? a) 3/4 b) 1/4 Oc) 10 d) 100 O e) 25
Course: Microeconomics - Intertemporal Consumption Decisions Consider a person who consumes in the 2 periods (C1 and C2), but ONLY works and earns an income in the first period (C1). Assume that consumption in each period behaves as a normal good.a) What is the effect of a rise in income on welfare? And on consumption in both periods? GRAPHb) What is the effect of a rise in the interest rate (assume that r goes from 10% to 15%) that occurs before the consumption decisions on welfare? GRAPH and on consumption in both periods?) GRAPH
please answer B
2. Utility maximization - Trading off labor and leisure The indifference curves on the following graph show Amy's preferences for leisure and consumption for increasing levels of utility, such that her utility increases in both consumption and leisure. Assuming that Amy spends 68 hours each week sleeping, she has a maximum of 100 hours available to her for leisure if she does not work at all. Initially, she works 45 hours (and thus has 55 hours of leisure) and earns $250 per week. Use the grey point (star symbol) to indicate Amy's initial leisure/consumption bundle. Dashed drop lines will automatically extend to both axes. ? CONSUMPTION (Dollars per week) 1000 900 800 700 600 500 400 300 200 100 0 0 10 20 30 40 50 60 70 80 LEISURE (Hours per week) 90 100 110 Initial bundle $200 Unemployment Benefits Equivalent Bundle, $100 Unemployment Benefits Equivalent Bundle Now, suppose that Amy is laid off, but she is eligible to collect unemployment benefits of $200 per week. Use the black point…
4. Steve's utility funetion over leisure and consumption is given by u(L,Y) = min (3L, Y). Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 5. Find the optimal leisure - consumption combination. What is the amount of hours worked? (b) Suppose the overtime law is passed so that every worker needs to be paid 1.5 times their current wage for hours worked beyond the first 8 hours. Will this law induce Steve to work more hours? If so, how many? If not, explain.
Question 35 Suppose real estate analysts expect that 100,000 homes will be needed in a particular community by 2014. If the current number of homes in the community is only 50,000, we can expect to see a significant increase in the demand for investment. True O False
8. (Continuing with the situation described in the preceding question.) Consider the economic model of an individual's labor-leisure choice with the following components: good w represents the hourly wage rate Y represents nonlabor income T represents total time available U(C, L) represents the individual's utility function MUC denotes the marginal utility of consumption MUL denotes the marginal utility of leisure Unless otherwise instructed, assume that consumption and leisure are normal goods. Whenever graphing the model, put C on the vertical axis and L on the horizontal axis. 4 C represents units of the consumption good L represents hours of leisure The individual maximizes his utility by choosing the optimal consumption bundle C*=90, L*=15, and H*=9. At this consumption bundle, MUC=4 and MUL=12. If p=2, what is w? 8 H represents hours of paid work p represents the unit price of the consumption O 10 O There is not enough information to determine w.
Suppose that the least amount of goods and services that Jim will consume in a year is $40,000. Jim tends to save $0.30 of every dollar of disposable income that he makes. Use the given line to graph Jim's consumption function for disposable income levels between $0 and $200,000. Move each endpoint to the appropriate spot on the graph.
1. Of the major costs of a typical family, which do you think differ most by geography and account for these purchasing power differences? (e.g. home prices/rents much higher in certain states (California, New York) compared to others (Mississippi))
11. A worker derives utility from consumption, C and leisure, L U = U(C, L) and initially faces the constraints p.C = N+w.H H = 24 - L where p is the nominal price of consumption, N> 0 is unearned income, w is the nominal wage and H is hours worked. (a) Derive the budget constraint in terms of C and L and show on a diagram an initial optimal choice of C and L, in which both are positive. (b) State this equilibrium algebraically, and briefly explain how it can be derived. (c) Show that, assuming normality of leisure, for some value N*, if N> N*, the individual will choose not to work. Is the initial level of N in your answers to parts a) and b) greater or less than N*?

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