Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a tax on the representative firm. The government collects t units of consumption goods from the firm for each unit of labor it employs (0

Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a tax on the representative firm. The government collects t units of consumption goods from the firm for each unit of labor it employs (0

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.6P

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Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the rep- resentative consumer. There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U (c, l) = α ln c + (1 − α) ln l (1) where 0 < α < 1 is a parameter. (a) Write down the definition of a competitive equilibrium for the above economy 1 (b) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, lump-sum tax, T , and output, Y in equilibrium. (c) Solve for the optimal allocation of leisure, l, the consumption, c, employment, N, output, Y . Contrast these quantities with those…
Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zND where Y is the output of the con- sumption good, z is the exogenous total factor productivity, ND is the labour hours. Government has to finance its expenditures, G, using a lump-sum tax, T, on the rep- resentative consumer. There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U (c, l) = α ln c + (1 − α) ln l (1) where 0 < α < 1 is a parameter. Answers for part b below: A consumer's choice of optimizing its consumption and labor hours (h - l ) is given by the point where , MRS(c , l) = wage rate Now , MRS (c, l) = MU(c) /MU(l) MU(c) = dU/d c = a/c MU(l) = dU /dl = (1-a )/l MRS = a (l)1−a (c)a (l)1-a (c) Putting this in optimal condition we have : a (l)(1−a) (c)a (l)(1-a) (c) = w --- (i) l = w…
– Consider the following one-period model. Assume that the consumption good is produced by a linear technology: Y = zN D where Y is the output of the consumption good, z is the exogenous total factor productivity, N D is the labour hours. Government has to finance its expenditures, G, using a tax on the representative firm. The government collects t units of consumption goods from the firm for each unit of labor it employs (0 < t < 1). There is no other tax in the economy. The firm is owned by the representative consumer who is endowed with h hours of time she can allocate between work, NS and leisure, l. Preferences of the representative consumer are: U(c, l) = ln c + ln l (1) ) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, tax rate, τ , and output, Y in equilibrium.
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?
Suppose that production function is Y=K1/3(AN)2/3 and competitive firms hire capital and labor to produce output. Let r be the return paid to capital and w be the real wage paid to labor. Which of the following is true? Group of answer choices A) a profit-maximizing firm hires capital and labor until average products equal factor prices B) labor income share is 1/3 C) real return to capital r grows at the rate of productivity growth D) real wages w grows at the rate of productivity growth
Consider a competitive, closed economy with a Cobb-Douglas production function with parameter α = 0.25. The parameter A is equal to 60. Assume also that capital is 100, labor is 100. Calculate GDP (Y) for this economy. Does the production function exhibit constant returns to scale? Demonstrate with examples. Determine if the production function exhibits diminishing marginal returns to capital. Demonstrate with calculus What is the real wage in this economy? What share of GDP will go to labor in this economy?
Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ? (Question 1: Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lb )
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.
Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ?
Consider now the two-period model in general equilibrium, so that prices, investment, and labor supply are endogenous, i.e. the production economy. Analyze and carefully explain graphically and in words the general equilibrium effects of a decrease in TFP for a benchmark economy with no frictions.
Answer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.
Consider the production function Y = z * K^1/3 * N^1/3 * L^1/3 where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land. Question text If we double the technology factor, z, then output will double. Question 17Select one: True False Question text If we increase the population, and therefore the workforce, then if nothing else changes, the average product of labour must increase. Question 18Select one: True False Question text We would need to increase capital input by a factor of 8 to double output. Question 19Select one: True False Question text Increasing technology will increase labour productivity. Question 20Select one: True False