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-3h¹t, where ß>0 and p > 0 are parameters. 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-3h¹t, where ß>0 and p > 0 are parameters. 1+p

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 simple economy consisting of two countries, England and France. England has 25 workers and France has 75 workers. England can produce 4 units of grain and 2 units of cloth with each unit of labor. France can produce 1 unit of grain and 1 unit of cloth with each unit of labor. Wages per unit of labor are the same in both countries. c. Assume that consumers have utility ?=?????^(1/2) ⋅????ℎ^(1/2). How much does each country produce and consume of each good in autarky? Show the consumption graphically by drawing the indifference curves into your two diagrams. d. Now allow for trade. How much does each country produce and consume of each good in this case? Draw the new production possibilities frontier, indifference curves, and equilibrium point into your two diagrams, and indicate exports and imports. e. What is the utility of consumers in each country under free trade? How much does utility change relative to autarky?
Find the utility-maximising levels of consumption and leisure. How much labour does the consumer - worker’s supply?
ASAP Suppose the consumer has the utility function U(C,l)=0.5 √C+√ l and has h = 24 hours available, some of which are used as leisure (l) and some supplied to the labor market (NS). Hours of work are paid at the real wage w. The profit income is π = 15. The consumer pays no tax. Writedown the budget constraint and the maximization prob- lem (a Lagrangian) and find the first order conditions for the consumer. Find an expression for the quantity of labor supplied
6 Assume you can work as many hoursyou wish at £12 per hour (net of tax). If you do not work you have noincome. You have no ability to borrow or lend, so your consumption,c , is simply equal to your income. d) Now assume that you receive an income of £140 per week from anunknown benefactor. Show the impact on your feasible set and show anew optimal choice in which consumption increases but labour supplydecreases. Using the concept of the marginal rate of substitution, explainwhy this is a likely outcome. Please illustrate on a diagram so I can better understand it please thank you.
please teach explain step by step
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-3h¹+, where 3 > 0 and p > 0 are parameters. 1+p
Let us denote Ben’s daily hours of work by H, and his hours of leisure by N = 24 − H. Suppose that Ben’s only source of income is wages for hours worked. He derives utility from leisure, N, and from the consumption of a composite good, Y. The price of Y is 1. Ben’s utility function is U(Y, N) = ln(Y) + ln(N). (a) Suppose the wage rate is $60 per hour. Write down Ben’s constraint with Y and N as the choice variables.
Question 2 - Consider a consumer with utility function U = x1 + x2 12, where is the labor supplied, x₁ and x2 are the quantity of consumption for good 1 and 2 respectively. The price of good 1 and 2 are p₁ and p2 respectively (P1, P2 > 0). The consumer cannot spend more than its earning from working, and has no other source of income. The consumer has an hourly wage rate of w. In the short-run, the consumer has signed a work contract that the work hour is fixed at ī> 0. The consumer cannot consumer negative amount of quantity of goods. a) Write down the constraints faced by the consumer in the short run. b) Find the utility maximising quantity of consumption for good 1 and 2 in the short run. Assume p₁ > P₂• c) In the long run, the consumer could choose the labour supply 1, i.e. I is not fixed and is a choice for the consumer. The consumer cannot work more than 24 hours a day, and cannot work negative amount of hours. Find the utility maximising quantity of consumption and labour…
6 Assume you can work as many hoursyou wish at £12 per hour (net of tax). If you do not work you have noincome. You have no ability to borrow or lend, so your consumption,c , is simply equal to your income. d) Now assume that you receive an income of £140 per week from anunknown benefactor. Show the impact on your feasible set (nb : be morecareful than Stephen was in his diagrams in Autumn Week 5!), and show anew optimal choice in which consumption increases but labour supplydecreases. Using the concept of the marginal rate of substitution, explainwhy this is a likely outcome.e)Now assume that, starting from the optimal point in d), your wageincreases to £18 per hour. Explain why the impact of this change isambiguous, and relate to the longrun historical experience of wagegrowth in rich countries. Please help me solve 6 e and illustrate on a diagram so I can better understand it please thank you.
Suppose that the owner of Boyer Construction is feeling the pinch of increased premiums associated with workers' compensation and has decided to cut the wages of its two employees (Albert and Sid) from $21 per hour to $17 per hour. Assume that Albert and Sid view income and leisure as "goods," that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Albert and Sid's opportunity set is presented below: Albert and Sid's Opportunity Set Income 0 5 10 15 20 25 30 Leisure Hours What is the value of A when the wage is $21? (Assume a 24-hour work day.) What is the value of A when the wage is $17? (Assume a 24-hour work day) At the wage of $21 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and equivalently supply 12 hours of labor). After wages were cut to $17, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure.…
9. Irene earns 8 dollars an hour. She has no nonlabor income. She has 30 hours a week available for either labor or leisure. Her utility function is U(c,r) = cr2, where c is dollars worth of goods and r is hours of leisure. How many hours per week will she work? а. 8 b. 13 с. 15 d. 10
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?