For a firm hiring both labor (L) and capital (C) under conditions of perfect competition, the equation that represents the Least Cost rule is: O MRCC = MRC, = MPc/MPL O MPC/MRPC - MRC /MPL 1 MRPL/MRC, - MRPC/MRCC 1 O MPL/MRC = MPc/MRCC
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- 1) The Cobb-Douglas production function is y = 12 with a > 0 and 3 > 0. Show that MP₁ = ay/2₁, MP₂= By/22. What is the MRT S21? How does it vary with: (a) y: (b) 2/1. 2) Show that the cost function for a firm with the constant returns Cobb-Douglas production function y = Actis given by C(p, y) = ypip-B, where B is a function of A and a only. Derive the conditional input demands.Peter's Pipers producers plumbing pipe. The long-run total cost of Peter's pipes is LTC = 20,000g- 200g +q° where Q is measured as thousands of feet of piping. The long-run marginal cost of Peter's pipes is given as LMC = 20,000 – 400q+ 3q || Exploit the relationship between LMC and LAC to find the quantity where LAC is at a minimum.The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) ina very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital isrented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production isGH¢1,000. Suppose the firm’s production function (Q) is as follows:? = 14?0.5?0.5 + 10Determine the optimal input usage and the maximum profit.
- 2. A production process using two inputs, labor and capital is Q = 5LK where Q is output per day. MPK = 5L and MPL = 5K. The wage (w) = $150 per hour and (r) = $1,000 per hour. Determine the least cost combination of K and L when the desired output is 1,000 What is the minimum cost of producing 1,000 per day?0.7 A firm has the following information on production and costs from past data: Output (Y) Total Cost (TC) If the total cost TC=aY³ + bY²+kY+f, and the demand for the product of the firm is Y = 320 - (1/2). P answer the following: ● 0 9 6 2775 18 8199 12 5361 function is known to be Determine the coefficients of the cubic cost function. Derive all cost and revenue curves and the profit function. Show that the MC cuts the AVC when AVC is at its minimum point. Plot the relevant graph indicating all points. Calculate the break even and profit maximizing levels of output and price. What is the relationship between price, marginal revenue and own price elasticity of demand at the profit maximization point.Your company's cost function (monthly) can be defined as; TC = cost per unit (AC) × quantity supplied (Q). If the cost per unit (average cost) for your firm is AC = (800/Q) – 10 +2Q: a. What is the total cost function for your firm in terms of Q? b. How would you interpret the intercept term in this function? c. What is the marginal cost function for your firm? d. At what level of output (Q) is AC minimized?
- A perfectly competitive rm produces output q with capital K and labor L according to the production function: q = f(K, L) = 4K 1 4L 1 4 The price of labor is w = 4, and the price of capital is r = 4. The rm has xed costs equal to 8. The current market price is 8. (a) Prove that this production function has decreasing returns to scale. (b) Find the optimal (cost-minimizing) ratio of capital to labor inputs K L for any level of output (use scale expansion path). (c) For any q, nd the cost minimizing inputs as functions of output: i.e., derive functions L(q) and K(q).A marginal profit curve equation is : MP= −2Q^2 + 160Q + 2145. You are required to determine the level of production, or range of production at which the company will have:(i) An increasing returns to scale(ii) A decreasing returns to scale (iii)A negative returns to scale (iv) Its maximum profitA competitive firm uses two variable factors to produce its output, with a production function q = min{x1, x2}. The price of factor 1 is £8 and the price of factor 2 is £5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of £80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount? А. £44 В. £41 С. £29 D. £13 Е. £21
- A competitive firm's production function is y =f(A,B) = 6A1/4B1/4. The firm can obtain as much of either factor as it (b) likes at factor rates wa = 3 and wB = 3. Find the cost function for producing y units of output for this firm (cost function in terms of y).A competitive firm uses two variable factors to produce its output, with a production function y = min{ x1, x2 }.The price of x1 is w1 = $8 and the price of x2 is w2 = $5. Due to a lack of warehouse space, the company cannot use more than 10 units of x1. The firm must pay a fixed cost of $80 if it produces any positive amount but doesn't have to pay this cost if it produces no output. What is the smallest integer price that would make a firm willing to produce a positive amount? please solve asap?Title is my answer for this question correct please advice me Description Making dresses in a labor intensive process. Indeed, theproduction function of a dress making firm is well described by theequation Q=L - L^2/800, where Q denotes the number of dresses perweek and L is the number of labor hours per week. The firms cost ofhiring an extra hour of labor is $20 per hour (wage plus fringebenefits.) The firm faces the fixed selling price, P = $40. a.) How much labor should the firm employ? What are itsresulting output and profit? b.) Over the next 2 years, labor costs are expected to beunchanged, but dress prices are expected to increase to $50. Whateffect will this have on the firm's optimal output? Explain.Suppose that inflation is expected to increase the firm's laborcost and output price by identical (precentage) amounts. Whateffect would this have on the firm's output. c.) Finally, suppose that MCL =$20 and P=$50 but that laborproductivity (output per labor hour) is…