1. An individual derives utility from the consumption of a basket of goods, $ c $, and leisure time, $ \ell $, given by\[U(c, \ell) = c^\alpha \ell^{(1-\alpha)}\]where $ 0 < \alpha < 1 $ is a constant. The individual must decide how to allocate her time between work, $ L $, and leisure to maximize her utility. The individual has a total of 24 hours in a day ($ L + \ell = 24 $), and total consumption is constrained by her income; i.e., $ c = wL $, where $ w $, the real wage per hour, is taken as given. **(b) What is the effect of an increase in $ w $ on labor supply? Provide a brief economic intuition.**(Note: There are no graphs or diagrams in the image.)

The income effect refers to the change in the quantity of a good that a consumer purchases as a…

1. An individual derives utility from the consumption of a basket of goods, c and leisure time, & given by U(c₂l) = cºl(¹-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L+= 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given.

1. An individual derives utility from the consumption of a basket of goods, c and leisure time, & given by U(c₂l) = cºl(¹-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L+= 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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When diminishing returns are present in consumption, the relationship between total utility and marginal utility is as follows: O Total utility increases at a decreasing rate while marginal utility decreases Total utility increases at an increasing rate while marginal utility increases Total utility increases at an increasing rate while marginal utility decreases Total utility decreases at a decreasing rate while marginal utility increases
EXERCISE 5 Loise spends £20 on tea (T) and coffee (C). Her preferences for these goods can be described by the following utility function: ( , ). Suppose that one cup of tea costs £1.60 while one cup of Loise’s favourite coffee costs £4.00. Find Loise’s optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. Discuss how Loise’s optimal consumption choice would change when her disposable budget changes. If the price of tea increases to £2.00 per cup, how should the price of coffee change so that Loise can be as well off as before this change in prices? Discuss the implications of the price change from c) on Loise’s optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Loise’s demand for tea and/or coffee.
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?
could you answer part e please
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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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3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.
Merge the two budget constraints into a single lifetime budget constraint by eliminating savings from the system of two constraints.
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