Assume that there is a representative firm in the economy. This firm takes the wage rate was givenand wants to maximize profits defined by π =4zNd-wNd. Nd is the labor demand of thefirm and z is a given productivity parameter. What is the optimal labor demand of the firm?○ Nd* = (3)Nd* = (32)43z4w○ Nd* = (%) 4○ Nd* = ( 32 ) 4 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 parameterBis positive, and 0 < ß < 1 holds.The consumer faces two constraints. The time constraint is given by 1 + N³ = 1 with N³ as thetime spent working (or the labor supply). Further, consumers take wages as given (outside of theircontrol) 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.=

Answered: Image /qna-images/answer/bab8e52e-3701-4cee-844e-bbc2ef264f96.jpg

Answered: Assume that there is a representative…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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This problem considers the decisions of a consumer whose preferences are given by u(C,1)=C+4 lnl, in which C' is the quantity of consumption and I is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1 with NS as the time spent working (or the labor supply). The main advantage of working is the wages consumers receive. Consumers take wages as given (outside of their control) and obtain wage income equal to wN³. The budget constraint is C wNsT, with π as real dividend income and T as the real = lump-sum taxes paid to government.
Task 4: leisure or work? The consumer choice is not restricted to the choice of consumption goods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has a wage per hour of 10 euros. With her earned income she consumes. That is, C = wH per day. She also decides how many hours to work of take leisure time each day. H = 24 – N, where H is work and N is leisure. Her utility is given by C1-o U(C, N) + B log(N) 1- o (a) Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif- ferent curve. What is the labor supply function? (b) If o > 1, what is the shape of the labor supply? How does it relate with the income and
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).
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)…
See attachment. This is not a writing assignment. I need to understand the mathematical steps to calculate the continuous rate of wine consumption, and also the number of wine bottles being consumed in the 30th year.
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
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…
Eren’s two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V^2MLast year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV).
The utility that Elena receives by consuming food F and clothing C is given by U(F,C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is£22. MUF = C+1 and MUc = F.(i) Define the term Marginal Rate of Substitution (MRS). (ii) Find the utility maximizing values of C and F for the numerical values given above(Hint: You can assume interior solution). (ili) Now suppose that price of C and Elena's income remain unchanged at £2 per unitand £22, respectively, while the price of F varies. Find the equation of the demand forF as a function of the unit price of F (PF).
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…

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