A firm uses labor (L) and capital (K) to produce output (q) according to the function: q= L ².K In the short-run, the firm's level of capital is fixed at one unit (K 1). Assume the firm has already paid a fixed cost of $1 (F = 1) for their one unit of capital. In addition, assume that each unit of labor must be paid a wage of $1 (w = 1). If the firm can sell each unit of output at a price of $6 ( p = 6), answer the following two questions: A) What is the firm's profit maximizing level of output in the short-run? Profit maximizing q 3 = B) What is the maximum profit the firm can earn in the short-run? Maximum profit 8 = dollars

A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.

The production function of Amazon burgers, producers of delicious burgers is given as Q =6L -0.4L². The unit price of burger is $10 and it costs Amazon $20 to employ a unit labor Required  How many units of labor should the firm employ to maximize profit if the firm is operating in the short run? Estimate the firm’s profit

Please help solve for (b) what is long run cost in a?

Consider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for production. The price of product is $p. The production function is Q (K; L) = 4L^1/4 K^1/4 . Assume that the hourly wage of workers is fixed at $w and the price per machine is $r Write out the optimal inputs quantities, L and K, as a function of parameters, p, w, and r

Suppose that the production function for Hannah and Sam's home remodeling business is Q=f(L,K) Q=1040.2K0.3 Assume the wage rate is $8,000 per week and the cost of renting a unit of capital is $2,000 per week. a. What is the least-cost input combination for remodeling 100 square feet each week? Instructions: Round your answers to 2 decimal places. units of labor and units of capital. b. What is the total cost? Instructions: Round your answer to 2 decimal places.

Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?

Subpart 1-3

Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100. Assume that this isoquant has a MRTS (marginal rate of technical substitution) such that an increase in L by 1 unit requires the firm to give up – ½ unit of K. Assume PL = $1 and PK = $1. What is the smallest total cost necessary to produce Q = 100?   $20 $10 $50 $100

A cost minimising firm has labour as its only input, but labour has two components, the number of workers, N, and hours per worker, h. Each worker hired incurs fixed costs (i.e. costs that do not vary with output), f, while the wage for “standard hours” (hours 3 up to and including 40 hours per week) is w per hour. For hours above 40 the firm must pay its workers an overtime premium of 50 percent, i.e. 1.5w. a) Derive the firm’s isolabour function (the function showing combinations of N and h which generate the same overall employee-hours). b) Derive the firm’s isocost function (the function showing combinations of N and h which generate the same total cost of labour). [HINT: it will have two “segments”, one for less than 40 hours per week and one for more than 40 hours per week.] c) Sketch the isolabour and isocost functions (with N on the y-axis and h on the x-axis). [HINT: to be able to show the isocost curve and know its shape, it helps to find out how its slope changes at the…