25.Consider a one-period closed economy model with government. The aggre-gate production is given byY = 2Nwhere N represents the employment and z is the total factor productivity.The consumer's preferences are given byU (C, 1) = ln (C) + In (1)subject to the following budget constraintC=w(h-1) +- Twhere denotes profits. The consumer has h units of time to split between laboursupply and leisure. The government spending is denoted by G and lump-sum taxesare denoted by T. The government's budget constraint is G = T.(g) Derive the equilibrium solution for output, Y*, and consumption, C*, in terms ofz, h and G.(h) Suppose that z = 4, h = 24, G = 5. Compute the equilibrium values of N*, w*, Y*, C*, T*.(Hint: You can use the Excel file used in class to verify your answers.)(i) If you use the social planner's problem, would you obtain the same solution?Briefly explain.

The social planner is a kind of benevolent dictator. His aim is that the consumers should receive…

(g) Derive the equilibrium solution for output, Y*, and consumption, C", in terms of z, h and G. (h) Suppose that z = 4, h = 24, G = 5. Compute the equilibrium values of N*, w*, Y*, C*, T*. (Hint: You can use the Excel file used in class to verify your answers.) (i) If you use the social planner's problem, would you obtain the same solution? Briefly explain.

(g) Derive the equilibrium solution for output, Y, and consumption, C", in terms of z, h and G. (h) Suppose that z = 4, h = 24, G = 5. Compute the equilibrium values of N, w, Y, C, T. (Hint: You can use the Excel file used in class to verify your answers.) (i) If you use the social planner's problem, would you obtain the same solution? Briefly explain.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 3E

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2 5. Consider a one-period closed economy model with government. The aggre- gate production is given by Y = 2N where N represents the employment and z is the total factor productivity. The consumer's preferences are given by U (C, 1) = ln (C) + In (1) subject to the following budget constraint C=w(h-1) +- T where denotes profits. The consumer has h units of time to split between labour supply and leisure. The government spending is denoted by G and lump-sum taxes are denoted by T. The government's budget constraint is G = T. (a) Solve the firm's maximization problem and derive the labour demand curve. (b) Graph the labour demand curve and explain its shape. (c) Show that profits are equal to zero, π = 0. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve.
Consider a dynamic (two-period) macroeconomic model with a representative household, a representative firm, and a government. The representative household makes consumption- saving and labor supply decisions. The representative firm makes labor demand and invest- ment decisions. (a) Clearly write down the representative consumer's problem and the necessary assump- tions. (b) Clearly write down the representative firm's problem and the necessary assumptions. (c) Clearly definite the competitive equilibrium for this economy. (d) Derive (graphically) the output demand curve. State the necessary assumption(s).
Be the production function Q (K, L) - : (K} +213), that depends on the quantitiess Used from inputs Kand L; and be the point (K, L) = (1,2). (a) What is the effect on the production of an increase of a unit in the amount used of INPUT L, L, Other things being equal?? (b) What is the effect on the production of an increase of 1% in the amount used of INPUT L, Ceteris paribus?
5. Consider a representative household in the static consumption-leisure model with prefer- ences given by u(c, 1) = Ac¹/² +1¹/2. The household has a unit time endowment given by 1 = 1+n, faces a price of P on consumption, and earns nominal wages at rate W on their labor supply, n. In addition, the household faces a proportional tax on wage income of T. (a) Interpret in words the economic significance of the exogenous parameter A. (b) Interpret in words the economic significance the unitary time endowment.
(a) Explain the characteristics of the production function used in the Heckscher-Ohlin (H-O)model. (b) Explain with the help of a graph how we can determine the specific combination oftwo goods that can be produced in the economy in the H-O model.
If the production function for GDP is Cobb-Douglas in labour and capital, with the exponent on capital is a space equals space 1 third, and assuming constant returns to scale, and a perfectly competitive goods market a. The marginal product of labour (vertical axis) will have a positive, concave slope when plotted against labour (horizontal axis) b. In equlibrium, wage will equal 2 over 3 y, where y is output per worker c. Labour and capital are complements so the derivative fraction numerator d squared Y over denominator d L d K end fraction less than 0 d. None of the answers is correct e. The marginal product of labour is: left parenthesis 1 minus a right parenthesis A open parentheses Lover K close parentheses to the power of a
1. Jason invests $5000 in a firm. The firm's production function is q = 10L0-¹K0.⁹. Workers cost $20 per unit and capital costs $100 per unit. a. If Jason wishes to produce the most output with the finances ($5000) available, how much labor and capital should he employ? Use a Lagrangian method for output maximization to solve this problem. b. Does this bundle of capital and labor also minimize the costs?
8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C₂) = (C₁) ¹ (C₂) ¹. We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual (b) Solve for the optimal allocation of (c, c) for all future generations. What the optimal k* ? Now suppose an…
8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C₂) = (C₁) (c₂) } . We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual (b) Solve for the optimal allocation of (c₁, c₂) for all future generations. What is the optimal k* ? Now suppose an…
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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) (a) Write down the definition of a competitive equilibrium for the above economy. (b) Show that the Walras’ law holds for this economy. (c) Solve for the leisure, l, the consumption, c, employment, N, wage rate, w, tax rate, τ , and output, Y in equilibrium. (d) Solve for the optimal allocation of leisure,…
xercise 5: Production and income distributionConsider and economy with the following production technology: ,Y = 9K1/3L2/3 wherethe aggregate capital stock is K=100, and aggregate labor is L=100. The price of output is1.a) Write down the maximization problem of the firm.b) Compute the equilibrium wage and capital return.c) Compute total payments to labor and capital. Show Euler’s Theorem holds, i.e. showthat total payments to capital and labor equal the value of output.d) What share of output goes to labor and capital?e) Suppose there is an increase in L, what would be impact on wages and capital returns?Explain.