The Nash bargaining solution between the employer and the worker satisfies the fol- lowing maximization problem: max[W (w) – U]°[J(w) – V]!-8, w where rW (w) = w+ s(U – W) and r.J(w) = y – w + s(V – J). Show that the outcome of this maximization problem is a surplus-sharing rule of the form: W (w) – U = B[W (w) – U + J(w) – V].
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- 3). . ; Consider the following Edgeworth Box, with consumers A and B and their respective indifference curves, endowment (@), and contract curve. a) Take points a and B. For each of these points, explain in no more than three sentences why or why not this point can be a Pareto equilibrium given the endowment w. b) Explain and show graphically how government policy can turn point y into a Pareto equilibrium.10. The figure below indicates the production functions and indifference curves in a job market signaling game. The worker has two type, High and Low ability. The receiver is a perfectly competitive market whose profits are driven to zero in equilibrium. Denote the education level choices by the High type by ey and the Low type by er. Let e* (L) and e* (H) be the equilibrium levels of education chosen by the Low type and the High type, respectively, in the full information case. In a separating Perfect Bayesian Equilibrium of this game IH y(H, e) wage y(L, e) education (a) eH = e*(H) and e, = e*(L). (b) en > e*(H) and e, = e*(L). (c) en = e*(H) and er > e*(L). (d) eH < e*(H) and e, < e*(L). 000 DD F4 F5 F6 E7 F8 F9 F $ % & 4 5 6 7 8 91993 12. Describe graphically with minimal (but necessary) discussion the Hicksian income/substitution decomposition that would lead to a perfectly inelastic demand curve.
- Two individuals, A and B, have the following utility functions UA = min {x^, y^} UB = min {x³, y³} and the endowments are of the same unit and quantity: x = y = 100. (a) Sketch the Edgeworth box and draw the contract curve. (b) If A has a different utility function UA = x² + y^ would the contract curve be different? Explain. (c) If we add the production of goods and y in the economy, and the technology is con- stant return to scale for both goods, can the competitive equilibrium still be achieved? Explained.3. In a competitive economy with many firms there are two types of workers that look ex ante identical. Low productive workers (type Ls) have an outside option of 0 (dollar or util), a utility function of "=w₁-2e,, where , is utility, w, is the wage received and e, is the education obtained. An L-type worker has a productivity of O. A high-type worker (H-type) has an outside option of 0, a utility function of w-e, where is utility, w, is the wage received and e the level of education obtained. An H-type worker has a productivity of 2. For the firms the workers look identical. However, firms can observe the level of education a worker has obtained. The timing of the game is as follows: workers decide how much education to receive; firms then observe the level of education of a worker and make a wage offer; worker can accept the offer (and work for the firm) or reject the offer and receive their outside option. a. What are the incentive compatibility constraints for the L-type worker and…Suppose that 2 agents, A and B, have preferences over goods 1 and 2: u+(x4) 2x + x5 and u (x³) = xFx. Total endowments are ej = B B Total endowments are e¡ = e2 = 4, (a) Find the contract curve. (b) If initial endowments are e4 = A (4,0) and eB (0, 4), what is the core?
- 7) Explain under which circumstances the compensated demand function is steeper than the Marshallian demand function (Use graphs if needed).Let the demand and supply function for a commodity be Qa= D(p,Y) Dp 0 Qs = S(p, w) Sp>0, Sw<0 where p is the price, Y in exogenous income, and w is the exogenous wage rate. a. Find dp and dp using the implicit-function theorem. dw dp dy b. Find and dp by totally differentiating the equilibrium condition. dwQuestion 2: Consider a competitive exchange economy with two individuals (A and B) and two goods (F and W). The total endowments of F and W are 10 each. Consumer A has the following utility function: UA = FW while consumer B has preferences such that she must have one unit of F for every unit of W. (a) Derive an expression for the contract curve and illustrate in an Edgeworth box dia- gram. (b) What is the relative price of F, PF/Pw, in a competitive equilibrium? (c) Now suppose that consumer B's utility function is UB = F +2W Let consumer A's utility function remain unchanged. Derive an expression for the con- tract curve now and illustrate in a new Edgeworth box diagram. (d) What is the relative price of F, Pr/Pw, in a competitive equilibrium?
- Ian works at an iron smelter in Pittsburgh, the center of iron production in America. Due to the difficulty in measuring the productivity of individual employees, Ian's employer as well as the other iron smelters all pay an efficiency wage. Adjust the wage line on the graph to reflect this situation. What characteristic of efficiency-wage jobs is not supported by the situation shown in the graph? Efficiency wage jobs result in a surplus of workers at the wage being offered. Elevated wages serve as an economic incentive to work harder. The wage rate will eventually return to the market-clearing level. Efficiency wages result in an increase in the rate of unemployment. Wage ($ per hour) Quantity of workers (in thousands) Wage SYvette currently earns a wage of $12.00 per hour; in other words, the amount of her paycheck each week is $12.00 per hour times the number of hours she works. Suppose the price of milk is $2.50 per gallon; in this case, Yvette's wage, in terms of the amount of milk she can buy with her paycheck, is gallons of milk per hour. When workers and firms negotiate compensation packages, they have expectations about the price level (and changes in the price level) and agree on a wage with those expectations in mind. If the price level turns out to be lower than expected, a worker's wage is than both the worker and employer expected when they agreed to the wage. Yvette and her employer both expected inflation to be 4% between 2012 and 2013, so they agreed, in a two-year contract, that she would earn $12.00 per hour in 2012 and $12.48 per hour in 2013. However, suppose inflation between 2012 and 2013 actually turned out to be 2%, not 4%. For example, suppose the…Government-Mandated Hiring Freeze. Echoing events in the U.S. from early 2017, suppose the government has set an economy-wide "hiring freeze." Operationally, the "hiring freeze" means that there is an upper limit V of job vacancies that firms can advertise in their recruiting process. More precisely, because the upper limit v is much smaller than the profit-maximizing value of job vacancies, firms will be subject to a “hiring freeze constraint" when determining profit-maximizing values for vacancies v and labor demand nº. The Lagrangian for the firm's profit-maximization is A f(n°)-w•n° –@•v+µ' (q° FIND v-nº)+2' · (V-v), hiring freeze constaint in which 2' stands for the Lagrange multiplier for the "hiring freeze constraint." All other notation is exactly the same as in Chapters 27, 28, and 29. For the sake of simplicity, there are no "long- lasting jobs" throughout this question – i.e., the job turnover parameter is fixed at p=1. a. Based on the Lagrange function stated above, compute…