Chopin loves to listen to his mother and sister playing piano, they are better piano players than him. He also loves to buy fancy clothing and to eat out. His utility of consumption and leisure is U = 0.210.8 where c is consumption of all other goods and I is leisure. If price of consumption is $1, wages are $2, and there are 24 hours in a day, answer the following questions. 1. %3D (a) Find Chopin's supply of labor in terms of hours. Hint: you can use big L to indicate labor. (b) Explain the substitution and income effects of a wage increase and the intuition behind it, No calculations needed.

Two individuals, Sam and Barb, derive utility from the hours of leisure (L) they consume and from the amount of goods (G) they consume. In order to maximize utility, they need to allocate the 24 hours in the day between leisure hours and work hours. The price of a good is equal to $1.00 and the price of leisure is equal to the hourly wage. We observe the following information about the choices that the two individuals make: Q 16- 14- 12- Sam Barb Sam Barb Price of Price 10- L L of L (hours) (hours) G ($) G ($) G 8- 7 13 10 77 98 1 132 1 11 10 12 154 1 15 7 14 255 150 6- Graphically, illustrate Sam's leisure demand curve and Barb's leisure demand curve. 4- 1.) Using the line drawing tool, draw Sam's leisure demand curve. Label this line D' 2- 2) Using the line drawing tool, draw Barb's leisure demand curve. Label this line D' 0- 0 4 в 8 10 12 14 Leisure (hours) Carefully follow the instructions above, and only draw the required objects. Wage (S)

Question 3: Shelly's preferences for consumption and leisure can be expressed as: U(C, L) = (C-200) × (L-80) This utility function implies that Shelly's marginal utility of leisure is C -200 and her marginal utility of consumption is L - 80. There are 168 hours in the week available to split between work and leisure. Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works. (a): Graph Shelly's budget constraint. (b): What is Shelly's marginal rate of substitution when L = 100 and she is on her budget line? Question 4: The utility function of a worker is represented by U(C, L) = C x L. Suppose this person currently has a weekly income of $600 and choose to enjoy 70 hours of leisure per week. How many ad- ditional dollars of income would it take to entice the worker to work 10 more hours?

Consider a worker who consumes one good and has a preference for leisure. She maximizes the utility function u(x, L) = xL, where a represents consumption of the good and L represents leisure. Suppose that this worker can choose any L € [0, 1], and receives income w(1 – L); w represents the wage rate. Let p denote the price of the consumption good. In addition to her wage income, the worker also has a fixed income of y ≥ 0. (a) Write down the utility maximization problem for this consumer. Solution: The problem is max x L s.t. px ≤w(1 L) + y. x>0, LE [0,1] The budget constraint may also be written with equality since preferences are monotone. (b) Find the Marshallian demands for the consumption good and leisure. Solution: Using FOCs will find the maximum since preferences are Cobb-Douglas (and therefore convex). Dividing the FOCs L= Xp and x = Xw gives wL = px. Substituting into the budget constraint and checking the restriction L = [0, 1], we get and x(p, w, y) L(p, w, y) = = = 1 w+y…

(Short Answers) 1. Jie works in a university. He can work as many hours as he wishes at a wage rate of w. Let C be the number of dollars he has to spend on consumption and let R be the number of hours of leisure that he chooses. Assume that Jie has the utility function U(C, R) = In(C) + In (R). He carms $4 per hour and has 80 hours per week to devote to labor or leisure, and has no income from sources other than labor.   a) How many consumptions does he choose? How many hours of leisure does he choose?   b) Suppose that Jie's wage rate will rise to $6 per hour from next year. How many hours of leisure per week will he choose next year? You are required to decompose his change in demand into the substitution effect, ordinary income effect and endowment income effect.   c) Suppose that Jie will get $4 per hour for the first 35 hours that he works and $6 per hour for every hour beyond 35 hours a week from next year. How many hours of leisure per week will he choose next year?

Consider an economy with two goods, consumption c and leisure l, 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 l = 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 T percent. The consumer 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 It hours of work can be represented by the utility function U(c, h) = c- (a) What is this consumer's budget constraint? (b) Solve for the consumer's utility maximizing hours of work h*(w, 1 - T, Y) and con- sumption c*(w, 1 - T, Y). (c) Repeat part (b) for a consumer with the utility function U(c, h) = alog(c) - Blog(h).

Consider an economy with two goods, consumption c and leisure I, 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 T percent. The consumer 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: h'+p U(C,h) = c-B- 1+ p where ß> 0 and p > 0 are parameters. TENTO COITS ar answer aneren ananm pally. p (j) Suppose instead that the consumer's utility function was U(c, h) = min(c, -h). Would the EB from a unit excise tax be larger or smaller compared with the original utility function. Explain your answer in 4 sentences.

Consider an economy with two goods, consumption c and leisure I, 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 T percent. The consumer 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: h²+p U(c,h) = c-B- where ß> 0 and p > 0 are parameters. 1+ P a) What is this consumer's budget constraint? (e) Suppose now that the income tax liability is increased to T = 0.3. Calculate the consumer's utility at their new utility maximizing consumption and labour supply bundle after the tax change. (h) Using the excess burden formula, calculate…

Consider an economy with two goods, consumption c and leisure I, 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 T percent. The consumer 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-B- where ß> 0 and p > 0 are parameters. ‚h¹- P 1+ p a) What is this consumer's budget constraint? b) Solve for the consumer's utility maximizing hours of work h*(w, 1-T) and consumption c* (w, 1 - T, Y). c) What is the compensated own-price elasticity for the supply of hours of work? For parts (d) - (h), assume the following: w = $50,…

Consider an economy with two goods, consumption c and leisure I, 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 T percent. The consumer 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: h¹+p U(C,h) = c-B- where ß> 0 and p > 0 are parameters. 1+ p (d) Suppose the income tax rate is initially zero (i.e. T = 0). Calculate the consumer's utility at their utility maximizing consumption and labour supply bundle. (f) Calculate the change in the consumer's surplus (i.e. utility) following the tax change. i) Now suppose that p = 1…