Consider an economy with a representative household that consists of = 100 workers and owns $81 million capital (L = 100; K 81). The representative firm with Y = K¹/2L¹/2 rents capital and hires labor from households. Assume A = 1 (TFP). Solve for equilibrium and enter the equilibrium quantities of Y, K, w, in the blanks below - Y = million K= million W =
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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.How do you know that the equillibrium prices are lower, the quantities produced are higher and the profits produced are lower in the merged scenarioSuppose that output is produced according to the production function Y = Kα[(1 - u)L]1-α, where K is capital, L is the labor force, and u is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate d. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the natural rate of unemployment (u). Write an equation that describes the steady state of this Find the steady state capital per worker and steady state output per worker. Does this production function have constant returns to scale?
- Suppose that output is produced according to the production function Y = Kα[(1 - u)L]1-α, whereK is capital, L is the labor force, and u is the natural rate of unemployment. The national savingrate is s, the labor force grows at rate n, and capital depreciates at rate d.a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and thenatural rate of unemployment (u).b. Write an equation that describes the steady state of this economy. Find the steady state capitalper worker and steady state output per worker.c. Does this production function have constant returns to scale? Explain.Suppose that output is produced according to the production function Y =Kα[(1 - u)L]1-α, where K is capital, L is the labor force, and u is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate d. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the natural rate of unemployment (u). Write an equation that describes the steady-state of this economy. Find the steady-state capital per worker and steady-state output per worker. Does this production function have constant returns to scale? Explain.Consider again the canonical OLG model with log preferences and a Cobb-Douglas production function, but assume that individuals now work in both periods of their lives. (a) Define a competitive equilibrium and the steady-state equilibrium. (b) Characterize the steady-state equilibrium and the transitional dynamics in this economy. (c) Can this economy generate overaccumulation?
- Land is a factor specific to producing olives. When Padua starts to trade, it exports olives. Using the specific factors model, explain what happens to nominal and real rental rates of land.State the assumptions of the 4th generation Keynesian model and explain how its endogenous variables are determined graphically Graphically demonstrate how to construct an IS(LM) curve. State the product market equilibrium condition, define an IS curve and explain why it is downward sloping.Consider now the two-period model in general equilibrium, so that prices, investment and labour supply are endogenous, i.e. the production economy. Analyse and carefully explain graphically and in words the general equilibrium effects of a decrease in TFP(total factor production) for a benchmark economy with no frictions.
- within the variable price fixed wage version of the keynesian model, analyze the effects of an increase in money demand (shift in liquidity preference) due to a loss confidence in stocks and bonds(Production function) A technological breakthrough raises a country’s A ̄ by 10%, but capital and labor are all unchanged. Assuming the country’s production function is given by Y = A ̄K1/2L1/2.(a) Figure out what impact this breakthrough will have on the MPK and MPL in that country. (b) Draw a picture Y of against K holding L fixed. 1 (c) Redraw the picture with A ̄ increased to 1.1A ̄ but L fixed at same level as before. (Production function) For the production function Y = K1/3L2/3 (a) find the function for output per capita (b) What is the growth rate of per capita for this function in terms of the growth rate of K, gK, and the growth rate of L, n.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…