Let the demand and supply function for a commodity be Qa = D(p, Y) Dp <0, Dy> 0 Sp>0, Sw<0 Qs = S(p, w) where p is the price, Y in exogenous income, and w is the exogenous wage rate. a. Find dp and using the implicit-function theorem. dy b. Find d and dw dp by totally differentiating the equilibrium condition. dw
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Could you explain again how you got part a? I don't understand what RHS is nor what the answer is for the partial derivative for price with respect to wage
- Determine whether the following statements are true, false, or uncertain. Please illustrate and explain your answer. If leisure is a normal good, then an individual's labor supply curve must be positively sloped. If leisure is an inferior good, then an individual's labor supply curve must be negatively sloped.A worker has 110 hours available in a week that can be used for leisure (L) or work (h). The utility function is U = (1 - α)ln(C) + α ln(L), where C is consumption. a) The price per unit of consumption is 1, the hourly wage is w, and the worker has a non-labor income of V. Show that the labor supply is: h* = (110(1-a)- (av)/w). Also, find the demand for consumption and leisure. b) What is the effect on labor supply of i) an increase in the hourly wage and ii) an increase in non-labor income? c) Set α = ½. What are C, L, and h when w = 200 and V = 10000? What is the reservation wage? d) What is the effect on labor supply of i) a 30% income tax and ii) a 10% wealth tax (on V)? e) What is the labor supply if V increases to 11600? f) An increase in V to 11600 gives the worker the same utility as w = 250 and V = 10000 (you do not need to show it). What are the income, substitution, and total effects on labor supply of an increase in wage from 200 to 250 while V remains at 10000?…Mac can trade off leisure for income. The rate at which he can do so is given by the wage rate. Mac is endowed with 24 hours per day. (a) Assume that leisure is a normal good. Construct Mac’s labor supply curve from an indifference curve/budget constraint mapping. (b) Now assume leisure is an inferior good. Construct Mac’s labor supply curve from an indifference curve/budget constraint mapping.
- For the following alternatives, argue whether it is true, false or uncertain, according to the following statement:"If the marginal productivity value (MVP) of the last worker hired is $10 and the wage is $12, then the firm":(a) Will have an economic utility.b) Needs to decrease the wagec) It needs to expand productiond) It needs to decrease the number of workers hired.Susan obtains utility by consuming carrots C and enjoying leisure L. Suppose that she has a daily non-wage income Y of £100 and is paid a fixed hourly wage rate of £10 for every hour she works in a local coffee shop. Assume that Susan is a utility maximiser and is free to choose x hours of work per day where 0 ≤ x ≤ 10. Assume also that the unit price of C is £1. a) Suppose that L is measured on the horizontal axis and C on the vertical axis. Use these axes to draw the set of all C and L combinations that Susan can choose from. Write down Susan’s budget equation. b) Suppose that Susan’s preferences over carrots and leisure are expressed by the following utility function: U(C,L) = min{C, 10L}. Calculate Susan’s optimal consumption bundle, both algebraically and graphically. Calculate the value of MRS at the optimal choice. c) Suppose instead that Susan’s preferences are such that indifference curves in the L-C space are strictly convex to the origin, and that she chooses to work 5…Consider a representative agent with the utility function U = ln(Ct)+ Nt The budget constraint is Ct = wtNt +Dt where wt is the wage and Dt is non-wage income (i.e. a dividend from ownership in the firm). The agent lives for only one period (period t), and hence its problem is static. (a) Derive an optimality condition characterizing optimal household behav- ior. (b) Solve for the optimal quantities of consumption and labor. Plz do fast asap, urgent.
- Consider a couple (a husband and a wife) that jointly represents their collective preferences between combinations of household production time (X) and purchased goods and services (Y) according to the formula W = X2Y, where W represents the level of welfare. Suppose the maximum time available in a day is 16 hours and currently the wife devotes 6 hours to market work (H) at a wage of $16 per hour. a. What is the level of welfare associated with the wife’s current situation? b. How much additional purchasing power would the wife contribute if her market work hours increased to 8? c. How much of an increase in purchased goods and services would be necessary to compensate for the additional 2 hours of lost household production? d. Should this couple choose to have the wife increase her market work by 2 hours? e. If this couple is raising a child, suppose that combinations of household production and purchased goods are now ranked according to the formula U = X3Y. Would the additional 2…Q1: Suppose Labor and Capital are substitutes and the price of capital falls. All else equal, we should expect the labor select (supply, demand) Curve shift select ( up to the right, down to the left ) and for equilibrium wages to select (rise, fall) Q2: An individual has a utility function over Leisure and Income such that ?=?1/2?1/2 This individual has a budget constraint ?=?⋅(24−?)+? The best possible wage this individual can earn in the labor market is $2 per hour. This individual is $30 in debt (they have negative non-labor income). If this individual is earning a utility level of 4, which of the following are true? Group of answer choices The worker could be supplying 1 unit of Labor The worker could be earning $10 The worker could be supplying 8 units of labor The worker is maximizing their utility given their budget The worker's Marginal Rate of Substitution at the point where the budget constraint intersects the indifference curve is equal to -2Consider the labor market in an imaginary coastal town called Nutsland. There is only one buyer in that market, namely Nutsland Farm that operates with a production function of Q= The supply of labor is given as L=w-2, where w is the wage. On the output side, Olive Farm takes the price P =20 TL/kg for its olive oil as given due to intense competition in that market. Find Olive Farm's profit-maximizing labor demand. What wage does it have to pay? What would be the wage in Nutsland if the market were competitive? Compare the welfare implications of a) versus b). Calculate the deadweight loss and show it on a graph.
- A worker receives, when unemployed, an offer to work forever at wage w, where w is drawn from the distribution F(w). Wage offers are identically and independently distributed over time. The worker maximizes Where ct is consumption and lt is leisure. Assume Rt is i.i.d. with distribution H(R). The budget constraint is given by And lt + nt ≤ 1 if the worker has a job that pays wt. If the worker is unemployed, the budget constraint is at+1 ≤ Rt(at + z − ct) and lt = 1. Here z is unemployment compensation. It is assumed that u(·) is bounded and that at , the worker’s asset position, cannot be negative. This assumption corresponds to a no-borrowing assumption. Write the Bellman equation for this problem.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 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?