What is the optimal labor supply of the representative consumer? ○ N³* = 1 − (3) 4 1-(3/4) 4w4 ON * = 1 - (38 β = 1 − ( ) ○ N8* = 1 - 4w ○ N** = 1 - (40) 43 Consider the decisions of a representative consumer whose preferences are given by u(C, 1) = C+ Bl₁, in which C is the quantity of consumption and 1 is the quantity of leisure. The parameter Bis positive, and 0 < ß < 1 holds. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1 with N³ as the time spent working (or the labor supply). Further, consumers take wages as given (outside of their control) and obtain wage income equal to wNs. The budget constraint is C w(1-1)+π-T, with TT as the real dividend income received from the representative firm and T as the real lump- sum taxes paid to the government. Assume for simplicity that T = 0. =

Consider the problem of a consumer who chooses between consuming goods and enjoying leisure in the current and future periods. Denote the consumption and leisure in the current period as C and l, and the consumption and leisure in the future period as C′ and l′, respectively. The preference is summarized by the following utility function: U(C,C′,l,l′)=lnC+ψlnl+β(lnC′ +ψlnl′). This individual is endowed with h units of time in each period. Wage rate per unit of labour time is w and w′ in the current and future period. In addition, the consumer receives profit transfer π and π′ and pays lump-sum taxes T and T′ in the current and future periods. Denote the saving in the current period as Sp. Answer the following questions. Derive the life-time budget constraint of this consumer.  Set up the consumer’s problem. Solve for consumption (C and C′), leisure (l and l′), and saving (Sp).  How does an increase in wage rate w affect C, Sp, and l?

Consider the decisions of a representative consumer whose preferences are given by: u(C,1) = In C+ Inl where C is the quantity of consumption and 1 is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1, with N³ as the time spent working (or the labor supply). Further, consumer take wages as given and obtain after-tax labor income that is equal to w(1t)Ns where t is the income tax rate (0 < t < 1). Thus the consumer's budget constraint is given by C = w(1 − t)(1 − 1) + π where is the real dividend income received from the representative firm (i.e. firm profits).

Deborah's utility over consumption (C), hours worked (H), and hours spent in commute (S) is: (1) U (C, H) = C¹2-H-S. The maximum number of hours that Deborah can work productively is 10. Thus (2) 0≤H≤ 10. On the days which Deborah works, she spends 2 hours in commuting from home to work and then back (one hour each way). (3) If H > 0, S = 2. Else if H = 0, S = 0. Assume that C ≥ 0 and S≥ 0. For simplicity, we also assume that there are no other costs (e.g., ticket costs, parking fee) associated with commuting. (a) Explain why Deborah's preferences are not strongly monotone in C and H. Use an example to support your answer. (b) Deborah's marginal utility from consumption (C) is strictly decreasing in C. True or False? Explain. Draw an indifference curve in (H, C) space that yields U = 6. Make sure to plot hours worked (H) in horizontal axis and (C) in vertical axis and label at least two points/bundles which give U = 6. (d) Deborah's income is hourly wage (w) times the hours worked (H).…

Consider the problem of an individual that has Y dollars to spend on consuming over two periods. Let c denote the amount of consumption that the individual would like to purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase cı units of the consumption good at a price P and can save any unspent wealth. Use sı to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the individual has at his/her disposal to purchase consumption goods in period 2 is (1+r)81. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2. 2 The individual's total happiness is measured by the sum of period utility across time, u(cı) + u(c2). Let u(c)…

An individual’s utility function is given by where is the amount of leisure measured in hours per week and is income earned measured in cedis per week.  Determine the value of the marginal utilities, when = 138 and = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?

Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t.  The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???

An individual values both consumption and leisure. Suppose the individual has 1600 hours per week they can allocate between leisure and work. IF the individual works, they make a wage of $25 per hour. The individual's utility function is given as a function of leisure time, L and consumption, c: U(L, c) = L^(1/2)c ^ (1/2) a) Draw the individual's budget constraint for leisure and consumption. b) How much leisure time will the individual have when utility maximizing? c) Consider a Universal Basic Income policy like the one proposed by Andrew Yang that would give all individuals a lump -sum, unconditional cash transfer of $1,000 each month. How much leisure time will the individual have when utility maximizing with the cash transfer? d) Now suppose, instead of a cash transfer, a minimum wage of $40 per hour is implemented. How much leisure time will the individual have when utility maximizing with the cash transfer? e) What change in leisure time can be attributed to the substitution…

Given the utility function U = x₁2/5x23/5; when x₁ = 100 and x₂ = 200; choose the correct options. A Consuming one more unit of x2 delivers higher value of Utility compared with an increase of consumption of one unit of x1 B Utility function is a constant returns to scale function. The proportionate change in utility is the same as the proportionate change in each input. Utility function is an increasing function Marginal utility with respect to x1 is equal to 0.1447 when x1 = 100 and x2 = 200 E Marginal utility function is an increasing function F None of the given answers is valid

A consumer has a utility function over consumption and leisure given by U(c, /) = In(c) + 4 In(/). The consumer is currently working 6 hours per day, is paid $15 per hour and the consumption good costs $5 per unit. Given this information, the consumer could increase their utility by %3D a. They are already at the optimal working hours b. We cannot determine whether they should be working more or less with the information given O c. Working less d. Working more Which of the following explanations for unemployment is inconsistent with the classical theory? a. Firms in a unionized industry cut workers as the union negotiates a higher wage b. A worker refuses to accept a job because they would rather wait for a better opportunity c. Workers choose to work fewer hours as unemployment benefits are generous d. Firms hold off on hiring new workers because they are worried that demand for their products will be low