Given the linear production function: Log (Q) = 1.5 + 0.76 Log (L) + 0.24 Log (K) Where Q is the level of output, L is the units of labor and K is the units of capital employed. a. If one worker's wages are $30 per day, how many workers should the firm employ per unit of output? b. What is the percentage of the firm's revenue spent on labor?
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Given the linear production function:
Log (Q) = 1.5 + 0.76 Log (L) + 0.24 Log (K)
Where Q is the level of output, L is the units of labor and K is the units of capital employed.
a. If one worker's wages are $30 per day, how many workers should the firm employ per unit of output?
b. What is the percentage of the firm's revenue spent on labor?
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- Why does the marginal product of labor start to decrease after a certain number of workers are hired? What makes the difference? a) The variable input continues to increase while the fixed input is fixed. b) Both the variable and the fixed inputs are increasing at the same rate. is it a or b?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?Calculate the Marginal Product (MP) at each input level. If the price of printer is $100 each, calculate the Value of the Marginal of labor (VMPL). If the wage rate (per week) is $1800 , how many workers will be employed? If the firm decides to hire 14 workers, what is the maximum wage the firm would be willing to pay?
- You are the owner of a puppet manufacturing company. Suppose that labour is the only variable input to the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labour?Widget factory Inc. in Wisconsin has the following production function: F(L,K)=2L L represents the number of labours hours. Workers at this factory are paid an hourly wage of $30 and they rent capital at$25/ hour.since this is a competitive market, the factory output is $50 per unit. Let's pretend the firm operates in the short run with capital fixed at 900, how many workers would widget factory Inc employ? What is their profit rate?Suppose that the production function for a phone is ? = 20K^0.5L ^0.5 . The marginal product of labor is 10(k/l)^0.5 , and the marginal product of capital is 10(L/K) ^0.5 . Suppose that labor can be hired for $6 and capital can be hired for $9. a. When the firm is producing 49 units at lowest cost, what will the firm’s marginal rate of technical substitution be? b. Solve for the lowest-cost combination of labor and capital that will allow the firm to produce 49 phones. Fractional units of labor and capital are allowed. c. What is the minimum cost of producing 49 phones?
- A firm produces good Y with just 2 factors: Capital which is fixed in supply and labour which is variable. Identify the stages of production in the diagram and explain why the firm still hire labour even though it is in the range of diminishing returns. What is the number of workers after which diminishing marginal returns starts? Is this a short run or long run phenomenon? Labour (units) 1 2 3 4 5 6 7 8 9 Total Product (TP) in Units 8 15 24 30 35 37 38 38 36 Average Product (AP) in units 8 7.5 8 7.5 7 6.17 5.43 4.75 4 Marginal Product (MP) in units 8 7 9 6 5 2 1 0 -2Assuming the firm is minimizing its cost and the price of labour is $10 per unit and the price of capital is $20 per unit. the marginal product of labour is 50, what must the marginal product of capital be?In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q = f(L,K), - ²³. q=6LK +4L² where q is output, L is workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MPL = (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.)
- Consider a firm that produces car repairs. All inputs are fixed except the number of workers hired to make repairs. The schedule of output as the number of workers changes is : Number of Workers Repairs Completed(per day) Marginal Product ( per day) of that worker 1 3 3 2 9 ? 3 18 9 4 30 12 5 ? 15 6 52 7 7 58 6 8…In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q = f(L,K), q = 6LK + 7L2 – where g is output, Lis workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MP, =. (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.) For example, if L = 5 and K= 23, then the marginal product of labor equals MP, =. (Enter a numeric response using an integer.) If L=9 and K= 23, then the marginal product of labor equals MP, =. (Enter a numeric response using an integer.) 20 tv MacBook Air S0 F2 F3 F4 % & 4 6 { E R Y P F G J K > C V M command option レ .. .- V * C B *3A firm’s only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X=-0.1L3 + 6L2 + 12L. Where X is the output in tons, and L is the number of persons employed. How many persons are employed if the average physical product of labour is maximized? How many persons are employed if the marginal physical product of labour is maximized? What is the quantity of X when average variable cost is minimized? If the weekly wage is $360 and the price of X is $30 per ton, how much X should be produced to maximize profits?
