We are supposed to do only four subparts to a question. For solution to other parts of the question please post as a separate question.
Problem 5 Assume that a worker has the Utility Function U(C,L) C "C" refers to consumption in dollars and &...
Suppose Tom has a utility function U=C*L C= consumption L= hours of leisure Tom has 100 hours to divide between work and leisure per week wage is $20/hr 1. Write down budget constraint in terms of consumption and hours of work 2.Tom make decisions on hours of work, leisure and consumption to max. utility. Explain why we can collapse this problem to one in which he chooses hours of leisure only 3. Find optimal hours of work and total consumption...
Problem #1: Optimal labor supply Clark gains utility from consumption c and leisure l and his preferences for consumption and leisure can be expressed as U(c, l) = 2(√ c)(l). This utility function implies that Clark’s marginal utility of leisure is 2√ c and his marginal utility of consumption is l √ c . He has 16 hours per day to allocate between leisure (l) and work (h). His hourly wage is $12 after taxes. Clark also receives a daily...
Clark gains utility from consumption c and leisure l and his preferences for consumption and leisure can be expressed as U(c, l) = 2(√ c)(l). This utility function implies that Clark’s marginal utility of leisure is 2√ c and his marginal utility of consumption is l √ c . He has 16 hours per day to allocate between leisure (l) and work (h). His hourly wage is $12 after taxes. Clark also receives a daily check of $30 from the...
Question 1: Households A household's utility over consumption C and leisure l is U - U(C,0) Cl 1. Plot the household's indifference curve for U-80 for values of C andlless than 20 (i.e. find the curve containing all combinations of C and ( such that U(C, 0) 80) The household has a time endowment of h=16 hours per day. The wage rate per hour is w 1.25. The household's labour income is therefore wNs, where N-h-l-16- l is the time...
John’s utility function is represented by the following: U(C,L) = (C-400)*(L-100), where C is expenditure on consumption goods and L is hours of leisure time. Suppose that John receives $150 per week in investment income regardless of how much he works. He earns a wage of $20 per hour. Assume that John has 110 non-sleeping hours a week that could be devoted to work. a. Graph John’s budget constraint. b. Find John’s optimal amount of consumption and leisure. c. John...
4. Let a person's utility function over consumption, X, and leisure, L, be given by U = XL2, SO MUx = L2 and MUL = 2xL.The individual may work up to 24 hours per day at wage rate, w = $10 per hour, and he has non-labor income of $50 per day. The price of x, px, is $5. (a) Find the utility-maximizing x and L. (b) Show that at the utility- maximizing quantities of x and L, the consumer's...
4.1 Cindy gets utility from consumption (C) and leisure (L), and has a weekly timebudget ofT= 110 hours. Her utility function isU(C, L) =C∗L. She receives$660 each week from her great-grandmother regardless of how much Cindy works.What is Cindy’s reservation wage? 4.2What is Cindy’s optimal labor supply (h) and consumption (C) if her wage is10 dollars per hour? Show your work.4.3 4.3 What is her optimal labor supply and consumption if her wage is 5 dollars perhour? What is her...
A worker receives a wage rate w and has L hours of leisure every day (the total endowment of hours is 24 hours per day). The government taxes his income at the constant rate T. The worker spends all his income. 1. Write a budget constraint of this individual and plot it. 2. Display graphically what is the optimal consumption-leisure choice for this worker. 3. Imagine that the government increases the tax rate to T 0 . What is the...
3. Suppose an individual has a utility function U=U(M,X)=10 MX^2, where U is her utility, M is her(daily) money income and x is her(daily) leisure hours. Each day, the individual needs 6 hours for sleeping and other essential personal matters 3. Suppose an individual has a utility function U = U(M,X) = 10 MX, where U is her utility, M is her (daily) money income and X is her (daily) leisure hours. Each day, the individual needs 6 hours for...
Let Tom's utility function be U(C, L) =C2+X×L2. Suppose he has 100 hours to split between work and leisure and he has no non-labor income. Derive Tom's optimal choice of consumption and leisure as a function of the wage and X. What is Tom's reservation wage?(Hint:Graphing an indierence curve before solving the problem might be useful.) *This is the correct utility function, copied directly from the homework.