Thanks to a (hopefully) long sequence of great decision by their ruler, the population feels additionally motivated creating a labor supply shock. If the production function of your kingdom is 10 still f(N=100 L- L', and now your labor supply is L, =200+54w: 9. 10. Find the equilibrium labor supply, wages, and the new full-employment output.
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- Consider the following model of a competitive labour market where both firms and workers have perfect foresight and symmetric information about the price level (that is, no misperceptions). Firms' technology is given by the production function y = a N ½ (production function) where a is a positive constant representing total productivity, N is employment and the elasticity of production to employed labour is 1/2. The government requires firms to pay pension contributions to the fiscal authority: the contribution is a small fraction x of the wage paid to each employed worker. Therefore, firms profits equal P y - W N - x W N and they are maximized taking the price level P, the nominal wage W, and the pension contribution rate x as given. Labour supply is given by: W = P b N where b is a positive constant. Answer all the following questions. a) Derive the labour demand schedule by solving the profit maximization problem of firms.Consider an economy which is divided into different sectors, each producing a differentiated product. Workers in each sector are organized in a trade union which monopolizes the supply of labour to all firms in the sector. Because of its monopoly position, the trade union in each sector may dictate the nominal wage rate to be paid by employers in that sector. However, employers are free to choose the level of employment. For simplicity, assume that the number of working hours for the individual worker is fixed, so total labour input is proportional to the number of workers employed. Workers in sector are educated and trained to work in that particular sector, so they cannot move to another sector to look for a job. If a worker fails to find a job in his sector, he therefore becomes unemployed. His real income will then be equal to the real rate of unemployment benefit . An employed worker in sector earns the real wage where is an index of the general price level, so his net income…Economics Modify the Lewis model and assume that there is a strictly positive marginal product of labor in the traditional sector. Use figures with production functions in the traditional and the modern sectors to show what the equilibrium is when no one wants to move away from agriculture. What assumptions do you have to make about production functions to arrive at the conclusion that fewer people will end up in agriculture? Use the same starting point as in the above question. Derive the demand for labor in the traditional and in the modern sectors. Show graphically what the characteristics of the equilibrium would look like when no one wants to change sectors.
- Suppose that the production function takes on the following form: Q = E3K If Capital is equal to 64, the price of output is p, r is the price of capital, and w is the wage rate, then determine the short run demand function for labor. How does Autor (2015) characterize the types of jobs that are most vulnerable to being made obsolete by automation? In the Autor (2015) article, what are the three main factors that augments or mitigates the effects of technological change.Assume we are in a Ricardian world, where there are 2 countries: Home and Foreign, 2 goods: x and y, and one factor of production: Labor(L). The labor unit requirements for production of each good and the aggregate labor supply in each country are given as follows: Home country: ax= 4, ay= 3, L= 2400 Foreign country: a*x= 10, a*y= 6, L= 3000 d) If there is no trade between Home and Foreign, what will the relative price of x in terms of y be in each country?Productivity Gains and Real Wage. Let us consider a closed economy with one final good whose price is normalized to one. The supply of labor by the representative household, NS, is fixed at Ñ, i.e., NS = Ñ. Labor supply (LS henceforth) is thus a vertical line in the (N,w)-space where w is the hourly real wage. The representative firm produces an amount Y of the the final good by using labor, N: Y = A ln N where A is labor productivity. (a) Provide an explanation to the insensitivity of labor supply to real wage in- creases (hint: make use of the substitution and income effects). (b) Derive labor demand (LD henceforth). Derive the equilibrium real wage, w*. (c) Show graphically the effects of a rise in labor efficiency, A. How does the equilibrium real wage vary?
- Consider an economy with the Cobb-Douglas production function: Y = 3K0.2L0.8 K = 140000; L=8000 Round answers to two places after the decimal when necessary. c. Now suppose that Congress, concerned about the welfare of the working class, passes a law setting a minimum wage that is 9 percent above the current equilibrium wage. Assuming that Congress cannot dictate how many workers are hired at the mandated wage, calculate what happens to the real wage, employment, output, and the total amount earned by workers. Real wages = $ Total output = d. Does Congress succeed in its goal of helping the working class? O Yes, Congress does succeed in its goal of helping the working class. units No, Congress does not succeed in its goal of helping the working class. Employment = Total earned by workers = $ workers e. Does this analysis provide a good way of thinking about a minimum-wage law? O No, this analysis does not provide a good way of thinking about a minimum-wage law. Yes, this analysis does…Suppose in a particular labor market, the demand for labor is given by the equation LD = 180 – 3W and that the labor supply in this market for native-born citizens is given by LN = 3W, while the supply curve of immigrants in this market is given by LI = 2W, where L represents the number of workers, W is the wage expressed in real terms. Finally, suppose the production function can be represented by ?=100√L a. Assuming immigration is entirely prohibited, what are the equilibrium wage and employment level in this market? b. What would be the equilibrium wage and employment level in this market if immigration were completed legalized? c. How many jobs do natives lose as a result of this immigration? How much aggregate income is lost? d. Assuming the costs of capital in this market are zero, find the total profits to firms before and after immigration. What is the change in total profits? e. Compute the total output of this market before and after immigration. How much total output does…Q1. Suppose we are given the constant returns-to-scale CES production function q = [k + l]1/ where krepresents capital and l represents labora. Show that MPk = (q/k)1 and MPl = (q/l)1 .b. Show that RTS = (k/l)1 ; use this to show that elasticity of substitution between labor and capital= 1/(1 – ).c. Determine the output elasticities for k and l; and show that their sum equals 1.Note: Output elasticity measures the response of change in q to a change in any input.Elasticity of output wrt k is eq,k = %q/%k = (q/k)*(k/q) or (q/k)*(k/q) or lnq/lnkSimilarly for elasticity of output wrt l, eq,ld. Prove that q/l = (q/l) and hence that ln(q/l) = ln(q/l)Q2. Suppose the production of airframes is characterized by a CobbDouglas production function: Q =LK. The marginal products for this production function are MPL = K and MPK = L. Suppose the price oflabor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital if the manufacturer wants to…
- 1d. Given the Input - Output matrices and the final demands, find the value of total production for each of the industries:Assume we are in a Ricardian world, where there are 2 countries: Home and Foreign, 2 goods: x and y, and one factor of production: Labor(L). The labor unit requirements for production of each good and the aggregate labor supply in each country are given as follows: Home country: ax= 4, ay= 3, L= 2400 Foreign country: a*x= 10, a*y= 6, L= 3000 a) What is the opportunity cost of x in terms of y in Home and Foreign? b) Who has the absolute advantage in which good? c) Who has the comparative advantage in which good? d) If there is no trade between Home and Foreign, what will the relative price of x in terms of y be in each country?Suppose that firms in the zipper industry have the production technology: F(K,L)=4K^(3/4) * L^(1/4)You know that the cost of labor is 27 and the price of zippers is 8. If the market is in a long-runequilibrium and zippers are being produced, what is the price of capital?