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 CUITS ar answer aneren hanm pally. pa (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.
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- Consider an economy with one consumption good, 100 identical consumers and 100identical firms. Each consumer is endowed with one unit of time and one unit ofcapital. The agent can spend time either working or enjoying leisure. A represen-tative consumerís utility function is u (x; l) = ln x + 2 ln l, where x is consumptionof goods and l is leisure. Each firm hires consumers to work and rents capital fromconsumers to produce goods: y = f (K; L) = K^1/2L^1/2, where L is the amount oflabor hired and K is the amount of capital rented. Both consumers and firms takegoods price p, wage rate w and rental rate r as given. Normalize p = 1. 1. Set up a representative consumerís utility-maximization problem.Derive the Marshallian demands for consumption and leisure as functions ofwage w and rental rate r 2. Set up a representative firm's profit-maximization problem. Writedown the first-order conditions regarding the choices of K and L 3. Set up all the market-clearing conditions. 4. Use the…Suppose that a consumer can earn a higher wage rate for working overtime. That is, for the first q hours that the consumer works, she receives a real wage rate of w1, and for hours worked more than q, the consumer receives a real wage of w2; where w2 > w1: Suppose that the consumer pays no taxes and receives no nonwage income. (a) Write the consumerís budget constraint. (b) Draw the consumerís budget constraint and show graphically her optimal choice of consumption and leisure. (c) Show that the consumer would never work exactly q hours. (d) Determine what happens if the overtime wage rate w2 increases to w22, where w22 > w2: Determine the effects on working hours. Explain your results in terms of income and substitution e§ects.Given the utility function: U = ln c + l + ln c’ + l’ and the budget constraint: w(ℎ−l)+(w′(ℎ−l′))/(1+r)=c+(c′)/(1+r) (see pictures of function and constraint) where c = current consumption, c' = future consumption, l = current leisure, l' = future leisure, and r is the market interest rate.Suppose that the current wage, w = 20 and the future wage w' = 22. a) What is the optimal value of current consumption, c? b) What is the optimal valueof future consumption, c’*?
- 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 suppliedConsider a two-period consumption saving model and let f1 and f2 denote the first and secondperiod consumption, respectively. Assume that the interest rate at which the consumer may lend or borrowis 10%. Suppose that a consumer’s utility function is x (f1> f2) = f1 + 20√f2= The consumer first periodincome is L1 = $100 and the present value of her income stream is $330=(a) What is the optimal consumption stream (consumption bundle) of this consumer?(b) Is this consumer borrower or lender? How much does she borrow or lend?(c) What is the effect of a reduction of the interest rate to 5% on the consumer’s optimal first-periodsaving? (Make sure to take into account the effect of the decline in the interest rate on the present value ofthe consumer’s income stream.)Assume that consumption and leisure are perfect complements, that is, the consumer always desires a consumption bundle where the quantities of consumption and leisure are equal, that is, C=L 1) (Denote the total hours of time available by h, the real wage by w, the real dividend income from firms by pi (π), and the lump-sum tax by T. Write down the consumer’s budget constraint. 2) Determine the consumer’s optimal choice of consumption and leisure. 3) Assume that there is an increase in w . Show how the consumer’s optimal consumption bundle changes. Explain with reference to income and substitution effects
- Consider an individual who receives utility from consumption, c, and leisure, l. The individual has L time to allocate to work, n, and leisure. The individual’s consumption is a function of how much he works. In particular, c = root n. The individual’s maximization problem is max U =ln(c)+θl subject to c = √n n+l=L where θ > 0. Solve the maximization problem. Hint: Substitute both constraints into the objective function.Consider an economy with 100 identical households and 100identical firms. Each household is endowed with one unit of time. Half of the households are endowed with equal shares of firm, while the rest areendowed with no firm shares. A householdís utility is u (x; r) = 2 ln(x*r^2) ,where x is consumption of goods, r = 1- l is leisure time and l is thehouseholdís labour supply. Each firm hires households to produce goodsaccording to technology y = L^1/2, where L denotes the labour input. Goodsprice p, wage rate w, and dividend income are all taken as given. Normalizew = 1. Do the following: (a) Derive the Marshallian demands, x (p, D) andr (p,D), where D is dividend. (b) Derive the firmís input demand functionL (p) and profit function pi(p). (c) List all the market-clearing conditions.(d) Calculate the equilibrium price pSuppose that a person has 2000 hours to allocate each year between leisure and work. a. Derive the equation of his budget constraint given an hourly wage of $(15)/hour. b) Graph his budget constraint line based on the equation you derived in part a. (Consumption (C) on the vertical axis and leisure (L) on the horizontal axis). Please make sure to include the value for the vertical and horizontal intercepts. c) Now suppose that the local government introduces an income guarantee program for single parents in which the income transfer is $10,000 per year if an individual does not work during that year (this dollar amount represents the benefit guarantee). If the individual decides to work, this transfer program imposes a 100% benefit reduction rate (e. g.. each additional hourly wage earned is reduced by 100%). Derive the new budget constraint equation that corresponds to this scenario. d) Draw the budget line that corresponds to the new scenario on a new graph. (Consumption (C) on the…
- no chagpt answer urgent. The marginal rate of substitution of current consumption for future consumption is A) the slope of the indifference curve. B) minus the slope of the difference curve. C) the downward slope of the budget constraint. D) the endowment point. E) the slope of the lifetime budget constraint.If preferences for pizza increase and the price of labor to produce pizza decreases, the equilibrium quantity of pizza will ____ and the equilibrium price of pizza will _____ . increase, increase decrease, be indeerminate increase, be indeterminate increase, decrease Assume an intertemporal budget constraint that shows how consumption can be traded off between two periods, t and t+1. Assume the consumer can save and borrow at the same interest rate of 10%. Assume the consumer collects income of $100 in each period. To gain an extra $10 dollars in period t+1, what must the consumer give up in period t? $11 $9.10 $1 $10 A convex indifference curve implies what type of behavior? diminishing marginal utility complementary goods perfect substitutes inferior goodsAssume an individual has a utility function of this form U(C, L) = 20 + 4(C*L)1/2 This utility function implies that the individual’s marginal utility of leisure is 2(C/L)1/2 and her marginal utility of consumption is 2(L/C)1/2. The individual has an endowment of V=$80 in non-labour income and T = 16 hours to either work (h) or use for leisure (L). Assume that the price of each unit of consumption good p=$1 and the wage rate for each hour of work w=$10. a. What is this individual’s optimal amount of consumption and leisure? b. Assume a cash grant welfare program is instituted which pays M = 20 dollars for individuals who do not work. Compute the new optimal labour supply for this individual under the welfare program. Assume that prior to the welfare program, p =$1, w =$10, and V =$80 (as in part c). Does the individual accept the welfare program and not work? Show why or why not.