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.(d) Set up the Lagrangian, solve the consumer's optimization problem and derive thelabour supply curve.

Consumption – Leisure Model: In this model the household determine how he allocate his time between…

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(hl) +-T where 7 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. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve.

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(hl) +-T where 7 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. (d) Set up the Lagrangian, solve the consumer's optimization problem and derive the labour supply curve.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION 39 The folllowing table shows data for a simple production function. Capital (K). Labor (L) 10 0 10 1 10 2 3 4 5 6 10 10 10 10 TP or Q AP MP 6 14 20 14 8 Assume that the cost of capital, PK, is $50 per unit, and the cost of labor, PL, is $100 per unit. Marginal cost, MC, is at minimum when labor, L, is equal to O2 units. O4 units. O 3 units. 5 units.
2. Production function: Y=8(K^.33)(L^.66) What if there is skill biased technological change that makes capital more productive relative to labor such that alpha or the exponent on K rises to .5 and the exponent on L falls to .5 a) What is the new equilibrium real wage (assume no change in the labor supply equation & K = 1)? Labor Supply= (w/p)^2 b) What is the new equilibrium R/P (assume no change in the capital supply equation & L = 4)? Capital Supply= 1000(R/P)
The following are correct descriptions about the concept of Marginal Productivity of Labor (MPL), EXCEPT: Question 1 options: MPL measures the extra production generated by adding one extra unit of labor. MPL initially increases and eventually declines as more units of Labor are added. From the producer's perspective, The optimal level of labor is the one when MPL = Market Wage and MPL is still Increasing. If MPL increases for any given amount of labor, it will lead to a shift up of the Demand for Labor.
1. A firm's production technology is Y = A * K^0.25 * L^0.75, where the technology level A=8. For such a production function the marginal product of capital is MPK = 0.25 * 8 * K^-0.75 * L^0.75 The firm is stuck with K=81 but is flexible on workers. If the price of the firm's output is P=20 and the cost of a unit of capital is R=8.33, how many workers should the firm have? Round your answer to the whole worker. The answer is 10. I just need to know how to solve it
All of these statements about the production function are true EXCEPT a) the curve features 3 distinct regions: increasing returns to scale, constant returns to scale, and diminishing returns to scale. b)the curve's shape matches and its description of the interaction between the graph's axes represents the law of diminishing returns c) it can be applied to many economic markets d) one variation is used to show the difference between firm and market specific risk
1) For the following functions of production, find the functions of conditional input demand and the cost functions a. q = A min(az,, bz2}; b. q = Azf z; C. q = azı + bz2 d. q = az, + b(lnz2) a, b > 0 A, a, b > 0 A, a, b > 0 a, b > 0 2) For A and D of Point 1, verify Shepard's lemma. 3) For B demonstrate that is possible to retrieve the supply function based on what has been developed so far, in this case, atb<1 www.
Suppose we have one consumer with a Cobb Douglas utility function for consumption, x, and leisure, R : u(x, R) = a ln a+(1-a) In R. The consumer is endowed with one unit of labor/leisure and there is one firm with a constant-returns to scale technology: a = aL. Determine r(p, w) and R(p, w).
The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C)=²1C²2 where co. ₁, and care constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co5, c, 0.25, and c₂-0.75. Assume sach unit of labor costs $25 and each unit of capital costs $75. With $70,000 available in the budget, devalop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. L, CZO € 70,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0S LS 3,000 and 0 s Cs 1,000. Round your answers to the nearest integer when necessary.) units at (L. C)=(
QUESTION THREE: PRODUCER THEORY 1. Suppose the production function for automobiles is given by q = kl - 0.8k² - 0.21² where q represents the annual quantity of bicycles produced, k represents annual capital input, and I represents annual labor input. a) Suppose k=10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many cars are produced at that point? b) Again, assuming k=10, graph the MP curve. At what level of labor input does MP₁ = 0 c) Suppose capital inputs were increased to k-20. How would your answer to parts (a) and (b) change? d) Does the production of automobiles exhibit constant, increasing, or decreasing returns to scale? 2. Supposing that the firm in (1) is a competitive firm and its production function is y = 10 + (x - 1,000)¹/3. The price of the input x is w = 1. (a) Show that the firm's total cost curve is C(y) = 1,000 + (-10)³. (b) Show that the minimum of the marginal cost curve…
sitier the production model studied in Chapter 4. Final output in the economy is pro- duced using capital K and labor L. The production function is: Y = ĀK'/³L^/5 Assume that the supply of all inputs are exogenous and equal to L and K. Perfectly compet- itive firms are price-takers and choose how much capital and labor to demand by maximizing profits. Let w and r denote the wage and rental rate of one unit of labor and capital respec- tively. (a) What are the 5 endogenous variables in this model? Also list the exogenous variables and the parameters and provide a brief explanation of each. (b) Show the first order conditions for labor and capital. Explain the intuition for why these conditions are optimal for a firm. Are there diminishing returns to these inputs in this model? ( (c) Show that the solution for output per capita can be written as y = Ak/5. Observed GDP per capita is 3 in this economy. Capital per person is 32. If Ā = 1, what does this model predict for GDP per person?…
Suppose the representative firm of the economy has a production function of the form F(K, N) = AKO.5N 0.5 The marginal product of labor is then given by MP N = 0.5AK0.5N –0.5 . The current capital 3. stock is K = 40. (a) Holding fixed capital at 40, draw a graph of output as a function of labor. What are some important features of this graph? (b) If A = 4 what is the Labor Demand Curve, ND(w), as a function of the real wage w? (c) Suppose labor is supplied inelastically with NS(w)= 10. What is the equilibrium wage w, employment level N, and full employment output Y ? (d) Suppose that productivity unexpectedly increases to A = 6. What is the new equilibrium wage w, employment level N, and full employment output Y ? (e) Depict this change graphically. Denote the original labor supply and demand curves by NS and ND respectively. Denote the new labor demand curve after the productivity shock by ND' . (Does not need to be to scale).
Problem B: The Production Model Consider the production model that we have seen in class with a production function for final output specified as Y = K1/4L3/4 Capital and labor available in the economy are, respectively, K = 40 and L = 50. B.1 Write down the profits maximization problem for firms in the production model (you can write profits in units of final output). Derive the first order conditions for the firm's maximization problem and provide the economic interpretation of the first order condition for labor. B.2 Please define the property of "Constant Returns to Scale" as we did in class. Does the production function above exhibit constant returns to scale? Show your computations. B.3 State the equations that constitute the competitive general equilibrium for the economy in the production model above. What are the variables that you need to solve for to obtain a solution to the equilibrium?