Consider an economy with two goods, consumption c and leisure 1, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of 7 percent. The con- sumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h)=c-3h¹te where 30 and p > 0 are parameters. C- 1+p'

Consider an economy with two goods, consumption c and leisure 1, and a representative consumer. The consumer is endowed with 24 hours of time in a day. A consumer's daily leisure hours are equal to 1 = 24-h where h is the number of hours a day the consumer chooses to work. The price of consumption p is equal to 1 and the consumer's hourly wage is w. The consumer faces an ad valorem tax on their earnings of 7 percent. The con- sumer also receives some exogenous income Y that does not depend on how many hours she works (e.g. an inheritance). The consumer's preferences over consumption and hours of work can be represented by the utility function U(c, h)=c-3h¹te where 30 and p > 0 are parameters. C- 1+p'

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Consider a household with a wealth endowment of $5, and a MB of consumption of $1.71, 1.53, 1.39, 1.29 and 1.23 for 1st, 2nd..... unit of consumption C. A firm faces MR at $1.66, 1.52, 1.42, 1.34 and 1.28, for the 1st, 2nd..... unit of capital, K. In this market, if the interest rate is 41%, then the demand for funds is units and the supply of funds is. units. O 2;2 O 2; 3 O 3:3 O 3: 2 (7
2. The standard model of consumer behavior assumes that income is exogenous. Of course, a person's income usually depends upon the number of hours the individual works. Suppose that an individual has T hours each day which can be allocated toward working time, H, or leisure time, L-that is, T = H + L. The individual earns w dollars for each hour worked. Then the individual's income is M + wH where M denotes any non-labor income. The individual has preferences over leisure time, L, and a consumption good, X, which can be represented by a quasi-concave utility function, U(X, L). The consumption good, X, can be purchased at the price Px. The individual seeks to maximize the utility subject to the constraints on time and money. (1) Formulate the individual's problem as an optimization problem with two constraints a time constraint and a money constraint. Derive the first-order conditions. Give an economic interpretation of the Lagrange multipliers. (2) The two-constraints problem can be…
P2
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.
3. Consider the economic model of an individual's labor-leisure choice with the following components: C represents units of the consumption good L represents hours of leisure H represents hours of paid work p represents the unit price of the consumption 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 graphi the model, put C on the vertical axis and L on the horizontal axis. What is the slope of the budget line? -(MUC/MUL) O-(MUL/MUC) O-W O -(w/p) O-(w+Y)/p
An individual can earn $12 per hour if he or she works. Assume that a person can work at most 24 hours per day times 30 days per month for a total of 720 hours. Thus, the axis intercepts, in the absence of any program, are 720 x $12 = $8,640 in consumption and 720 hours of leisure. Scenario: Suppose that a new welfare program is introduced where the government guarantees $600 per month in income and reduces the benefit by $1 for each $1 of labor income. Below are the budget constraints that show the monthly income-leisure trade-off. Monthly income $8,640 $600 720 Leisure (hours) With 40% reduction rate, when he/she works 30 hours, where will he/she maximize his/her utility? O A. Point B O B. Point C O C. Point D O D. Point F
3. Consider a model where a consumer, Mehdi, is deciding how to allocate their 24 hours each day between work and leisure. The take-home wage they initially receive is w = 15, but following a rise in income tax, their take-home pay falls to w = 12. Following this change in the wage rate, Mehdi reallocates his time between work and leisure, as shown in the diagram below. Composite good 41 42 43 Time Constraint 24 Leisure (0-24)/ Work (24-0) Given this information, which of the following conclusions can we reach? (a) The substitution and income effects both cause Mehdi to take more leisure time, meaning leisure is a normal good. (b) The substitution effect and income effects both cause Mehdi to take less leisure time, meaning leisure is a normal good. (c) The substitution effect causes Mehdi to take more leisure time, while the income effect causes Mehdi to take less leisure time, meaning leisure is an inferior good. (d) The substitution effect causes Mehdi to take more leisure time,…
2. Let an individual’s utility function be given by where C and L are consumption and leisure respectively, and g, a and b are positive constants with a + b = 1. Derive the individual’s Marshallian labor supply function and comment on the magnitudes of the income and substitution effects of wage change. Derive the general form of Slutsky equation of labor supply.
QUESTION 7: Budget constraints Everyone is endowed with 168 hours in a week (24X7). If you work 40 hours or less, you w=$20 per hour. If you work overtime, you earn w-$25. Assume the worker has M= non-labor income and that the price of the consumption good is p. Draw the budget constraint. Label the intercepts and the slopes in both the overtime and non-overtime region.