In an economy, the total output of all the firms is described by Y = 8 * K^0.25 * L^0.75. For it, The price level is P=20 and the cost of a unit of capital is R=6. There are L=10 workers in the economy. The payments for capital, or the capital bill, amount to RK=752 in the economy. Find the payments for wage, or wage bill, WL, in the economy.
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1) In an economy, the total output of all the firms is described by Y = 8 * K^0.25 * L^0.75. For it,
The price level is P=20 and the cost of a unit of capital is R=6. There are L=10 workers in the economy.
The payments for capital, or the capital bill, amount to RK=752 in the economy.
Find the payments for wage, or wage bill, WL, in the economy.
The answer is 2258, I need assistance with how to solve and get that answer
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- A firm's production function is: q = 20L1/2K1/2 where q is the firm's total product, L is the quantity of labor employed, and K is the quantity of capital employed. The price of labor is $25 per unit and the price of capital is $100 per unit. a. What is the equation for the marginal product of labor? b. What is the equation for the marginal product of capital? c. Given the price of labor is $25 per unit and the price of capital is $100 per unit, what is the cost-minimizing combination of capital and labor that can produce 800 units of output?2. Consider a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among the workers). The production function Y = K2/6 L3/6 H1/6 a) Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor? (Hint: The marginal product of labor MPL is found by differentiating the production function (Y) with respect to labor (L)) b) Derive an expression for the marginal product of capital. How does an increase in the amount of human capital affect the marginal product of capital? (Hint: The marginal product of capital MPK is found by differentiating the production function (Y) with respect to capital (K)).Firm XYZ produces specialty widgets using labor and capital. The table below shows the productivity of both resources. The initial cost of a worker is $10 and the cost of capital is $20. Workers Total Product (Labor) Marginal Product of Labor Marginal Product of Labor per dollar W = $10 Marginal Product of Labor per dollar W = $5 Capital Total Product (Capital) Marginal Product of Capital Marginal Product of Capital per dollar P = $20 0 0 - - 0 0 - - 1 500 500 1 1,000 1,000 50 2 900 400 2 1,900 900 45 3 1,200 300 3 2,700 800 40 4 1,400 200 4 3,400 700 35 5 1,500 100 5 4,000 600 30 a. Complete the Marginal Product of Labor per dollar when the wage is $10. b. When the wage is $10 and the cost of capital is $20, what is the least cost method for producing at least 2,200 specialty widgets? unit(s) of labor and unit(s) of capital. c. Suppose the wage rate falls to $5. Complete the Marginal Product of Labor per dollar when the…
- Some economists believe that the US. economy as a whole can be modeled with the following production function, called the Cobb-Douglas production function: Y = AK¹/32/3 where Y is the amount of output K is the amount of capital, L is the amount of labor, and A is a parameter that measures the state of technology. For this production function, the marginal product of labor is MPL = (2/3) A(K/L)¹/³. Suppose that the price of output P is 2, A is 3, K is 1,000,000, and L is 1/100. The labor market is competitive, so labor is paid the value of its marginal product. a. Calculate the amount of output produced Y and the dollar value of output PY. b. Calculate the wage W and the real wage W/P. (Note: The wage is labor compensation measured in dollars, whereas the real wage is labor compensation measured in units of output)A production function is given by q = 500L + 320K. The price of capital is $120 and the price of labor is $100. What is the marginal product of capital divided by the price of capital? Answer to two decimal places.5. A company that produces auto parts has a production function of Q = 300 L-75 K-5. %3D If L= 250 and K= 25, what is the output of auto parts? If L increases to 350, what is the output of auto parts? What does the change in output show regarding labor as a factor of production?
- In Example 6.4, wheat is produced according to the production function: | = 100 (K°-$L05). Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. (Round your responses to two decimal places.) The MPK at 5 units of capital is 156.52. The MPK at 6 units of capital is 142.89 The MP, at 50 units of labor is 14.14. The MP, at 51 units of labor is 14. Does this production function exhibit increasing, decreasing, or constant returns to scale? A. Decreasing returns to scale because the inputs exhibit diminishing marginal returns. B. Increasing returns to scale because the inputs exhibit diminishing marginal returns. C. Constant returns to scale because a proportionate increase in all inputs results in the same proportionate increase in output.2. (Textbook problem 6, page 104) Suppose that the production function is Y = 9K 0.5 Nº.5. With this production function, the marginal product of labor is MPN = 4.5K 0.5 N -0.5. The capital stock is K = 25. The labor supply curve is NS = 100[(1-t) w]², where w is the real wage rate, t is the tax rate on labor income, and hence (1-t) w is the after-tax real wage rate. a. Assume that the tax rate on labor income, t, equals zero. Find the equation of the labor demand curve. Calculate the equilibrium levels of the real wage and employment, the level of full-employment output, and the total after-tax wage income of workers. b. Repeat part (a) under the assumption that the tax rate on labor income, t, equals 0.6. c. Suppose that a minimum wage of w = 2 is imposed. If the tax rate on labor income, t, equals zero, what are the resulting values of employment and the real wage? Does the introduction of the minimum wage increase the total income of workers, taken as a group?Suppose you are considering hiring another worker. Also assume that you are at a firm that is operating at a point where the marginal product of labor is 5 and the price of each unit of labor is $2, and the marginal product of capital is 20 and the price of each unit of capital is $10. Should you hire another worker? If you hire another worker, what will happen to the marginal product of labor and why?
- 1/3 1/3 Badgett's Gadgets produces gadgets with the production function, y = x, where x1 is the quantity of labor input, 2 is the quantity of capital input, and y is the 1/3 quantity of output. In the short run, Badgett's capital input is fixed at x=8, and so its short run production function is y = 3(8)¹³ = 2z/³. The per-unit price of labor input is w₁ = 20 and the per-unit price of capital input is w₂ = 40. If Badgett's is a price taker in the output market and can sell as many gadgets as it wishes at a per-unit price of p, what is the lowest value of p at which Badgett's is able to earn positive profits in the short run? Badgett's will earn positive profits for any p > 40. Badgett's will earn positive profits for any p > 80. Badgett's will earn positive profits for any p > 0. Badgett's will earn positive profits for any p > 120.Tausha and Alicia own a coffee shop in town. Their output (cups of coffee per week) in terms of labour and capital is Q=4L^0.5K^0.5 The Marginal Product of Labour is: MPL=2L^-0.5K^0.5 The Marginal Product of Capital is: MPK=2L^0.5K^-0.5 The wage per week is W=100 and the cost of capital per week is R=25. a) Find the MRTS LK and the tangency condition between their isoquant and isocost line b) What is the cost minimizing amount of capital and labour that produces 400 cups of coffee per week?Consider the following production function: Q = 2K + 5L. The price of capital is €10 per unit and the price of labour is €20 per unit. The firm wants to produce 100 units of output. The number of units of capital that the firm will hire is A. 50 B. 5 C. 25 D. 0