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- Q5 A firm's production function is Q is equal to 5L2Ka) Find out the MPL and MPb) Does this production function exhibit constant, increasing, or decreasingreturns to scale?c) What is the marginal rate of technical substitution of L for K for thisproduction function Q6.Suppose the firm sells its output according to the following demand scheduleMarginalTotal Product Total Revenue eLabor Product Price Revenue Product$3.50192c2.80182.30291.80391.65471.5021.4053Fill in the remaining two columns of the table. How many workers wilhired at a wage of $72A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?I am having trouble finding out the formulas to complete this question: The production function for a firm is q = -0.6L3 + 18L2K + 10L where q is the amount of output, L is the number of labor hours per week, and K the amount of capital. The wage is $100 and the rental rate is $800 per timeperiod. Using Excel, calculate the total short-run output, q(L), for L = 0, 1, 2, …, 20, given that capital is fixed in the short run and K = 1. Also calculate the average product of labor; APL, and the marginal product of labor, MPL. For each quantity of labor in (a), calculate the variable cost, VC; the total cost, C; the average variable cost, AVC; the average cost , AC; and the marginal cost, MC. Using excel, draw the AVC, AC, and MC curves in a diagram. You will not be able to solve the total product curve for L as a function of output. So, instead construct a table. Headings: L q(L) APL MPL VC TC AVC AC MC w/APL w/MPL
- Choose an answer 8. A production function with the character Decreasing Return to Scale (DRTS) means that if the production scale is doubled, the output will be a. Increased twofold c. It has more than doubled b. Increased less than twofold d. Neither is true 9. If the own-Pice elasticity of supply is 0.8, then ……. A decrease in P will decrease Q by as much as ……… a. 10%, 2% c. 8%, 10% b. 8%, 2% d. 10%, 8%The weekly revenue from the sale of a product is increasing at a rate of \$10$10 per \$1$1 increase in price, and the price is decreasing at a rate of \$0.5$0.5 per additional product sold. What is the marginal weekly revenue with respect to the number of products sold? Interpret your answer and be sure to state the units.A firm engaged in the manufacture of RTWS faces the short-run production function Q = 250L - 5L², where L is the number of units of labor and Q is the number of RTWs produced annually. d.) How many RTWS can be produced by the firm in a year if there are 10 units of labor? e.) Compute the marginal product of the 40th unit of labor. f.) How many RTWs can be produced by the firm in a year if there are 40 units of labor? g.) Sketch the graph of the production function.
- A firm's production function is: q = 16L1/2K1/3 where q is the firm's hourly total product, L is the quantity of labor employed, and K is the quantity of capital employed. Assume that the quantity of capital employed is fixed at 125 units per hour. The labor market is perfectly competitive, and the current wage, w, is $10 per hour. The firm sells its product in a perfectly competitive market and the price is $5 per unit. a. What is the firm's value of marginal product of labor? b. What is the firm's profit maximizing quantity of labor?Q1.The following is a Cobb-Douglas production function: Q = 1.75K0.6L0.5. What is correct here? * -This production function displays constant returns to scale -This production function displays increasing returns to scale -A one-percent change in L will cause Q to change by one percent -This production function displays decreasing returns to scale Q2. For studying demand relationships for a proposed new product that no one has ever used before, what would be the best method to use? * -consumer surveys, where potential customers hear about the product and are asked their opinions -double log functional form regression model -ordinary least squares regression on historical data -market experiments, where the price is set differently in two marketsTake a Cobb-Douglas production function, find its Elasticities w.r.t output and Elasticity of Substitution with the help of partial derivatives.
- Consider a production function for an economy with 2 factors of production L, K: Y=10(KL)1/2 where Y is real output, L is labour, K is capital. In this economy the factors of production are in fixed supply with L = 10, K = 10. What type of returns to scale does this production function exhibit. Demonstrate by example. If the economy is competitive what is the total income that will go to the owners of capital?Consider the following short-run production function: ܳ = −0.5L^2 + 10L. Suppose that the output of the firm can be sold at a price of $10. Also suppose that labor can be hired for $20.a) Find the marginal revenue product function.b) Find the amount of labor that should be hired to maximize short run profits.c) Suppose that the productivity of your workers increases. What happens to the demandfor labor hours? For illustration, suppose that the productivity increase changes the shortrun production function to ܳ = −0.5L^2 + 12L. Find how many workers are hired now.Suppose a firm has a production function with two inputs, capital (K) and labor (L). The production function takes the form: Q = L2K2. Further, let the wage be given by w, the rental rate of capital be given by r, and suppose that the firm wishes to produce Q0 units of output. Determine the elasticity of substitution for this production function. Explain your answer. Determine the returns to scale for the production function. Solve for the long-run optimal input demand functions for capital and labor as a function of exogenous variables only. Derive an expression for long-run total cost as a function of the exogenous variables. Let w=16, r=25, and Q0 = 10,000. Solve for the long-run cost-minimizing input combination.