6. Given the following diagram and the information that input a is the only varı- able input, answer the questions in parts a through d. Output| TPa 120 90 60 30 10 15 20 30 Input a a. What is the maximum value of AP,? b. At approximately what quantity of input a will MP, be at a maximum? c. If P is $96, what is the minimum AVC? 4.84-96 TFC480o hnd STCA SAC at ofp levelg60 units
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- Your product sells for $5 per unit, labor costs $5 per unit, and the rental price of capital is $20 per unit. Complete the following table, and then answer the accompanying questions. (1) (2) (3) (4) 5 6 L K Q MPL P VMPK 0 5 0 1 5 10 2 5 30 3 5 60 4 5 80 5 5 90 6 5 95 7 5 95 8 5 90 9 5 80 10 5 60 11 5 30 b. Which inputs are fixed inputs? Which are the variable inputs?c. How much are your fixed costs?4. A bottling company uses two inputs to produce bottles soft drink sludge: bottling machines (K) and workers(L). The machine costs $1000 per day (r) to run and the workers are paid $200 per day (w). At the current level of production, the marginal product of the machine is an additional 200 bottles per day (MPK), and the marginal product of labor is 50 bottles per day (MPL). a. State the rule for determining the cos- efficient combinations of inputs (K & L) for the production of soft drinks. b. Given r=$1000 per day, w=$200 per day, (MPK)= 200 bottles, and (MPL)= 50 bottles, is the company operating cost-efficiently? c. What must the company do to move toward cost-efficient operation? Hint: use more labor or more machines and why?1. The production function for the personal computers of DISK, Inc., is given by q = 10K0.5L0.5,where q is the number of computers produced per day, K is hours of machine time, and L ishours of labor input. DISK’s competitor, FLOPPY, Inc., is using the production function q = 10K0.6L0.4. a. If both companies use the same amounts of capital and labor, which will generatemore output?b. Assume that capital is limited to 9 machine hours, but labor is unlimited in supply. Inwhich company is the marginal product of labor greater? Explain.
- Suppose there are two inputs for production, labor and capital. The firm’s production process isdefined by the following production functiony=f(L,K).Howdoweinterpretthefirm’smarginalrateof technical substitution? a)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same cost level b)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm produces one more unit of output c)How many units of capital the firm would have to give up in order to attain one more unit oflabor, such that the firm maintains the same level of production d)a) and b) are correct e)a) and c) are correctComplete the table directly below by calculating MP and AP. Inputs ofL TP MP AP 0 01 152 343 514 655 746 807 838 82 Plot the TP, MP and AP and explain in detail the relationship between eachpair of curves. Explain why PM first rises, then declines, and ultimatelybecomes negative.3. Theo employs labor at a competitive wage (W) of $3 per unit, and he employs capitalat a competitive rental rate (R) of $6 per unit.a. State the cost-minimizing rule. You must provide both a written statement of it, and state it as anequation.b. At Theo’s current combination of labor and capital, the marginal product of labor (MPL) is twiceas large as the marginal product of capital (MPK). Is Theo currently employing the optimal ratio oflabor and capital? If not, how should he adjust his hiring of labor and/or capital? Explain.
- 1. Margeʹs Hair Salon production function is Q = f(K, L) = K0.5L0.5 where K is the number of hair dryers and L is the number of labour hours she employs. At the moment, Marge uses 16 labour hours and 16 hair dryers. Suppose that Marge can use any amount of either input without affecting the market costs of the inputs. If Marge increased her use of labour hours and hair dryers by 10%, how much would her production increase?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 itCOURSE: MICROECONOMICS - PRODUCTION THEORY Suppose a company engaged in manufacture of wheat whose production function is represented by: Q =10KL.In addition, firm must pay wages of $200 and rent on capital is $600. It is known that firm has a budget of $30,000 for cheese production.a) Calculate break-even point of both factors of production and graph itb) What will happen if minimum wage is now fixed at $300? Graph itc) Assuming that new minimum wage at point b) is maintained and, assuming that investor demands a capital rent of $900, explain what happens to optimal factor level. Graph it
- A 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?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 marginal product of effort, a typical worker in fast-food burger joint, is one- fourth burgers per hour; that is, MPe = .25The price of a burger is $2. The figure graphs Mac’s marginal cost of effort. If Mac increases his effort by one unit per hour, the change in the burger joint’s revenue is $ per hour. That is, what is VMPe , the value of Mac ‘s marginal product of effort ? Plot the VMPe curve in the figure. Mac efficient effort e^ is the solution to what equation? Illustrate the solution in the figure. Mac efficient…