A grave digging firm hires 2 daily workers (L) at a wage (w) of $20, and has 4 units of capital (K) at a rental rate (r) of $25. If the grave digging company is minimizing costs, w of the following production functions would result in this hiring mix? a.q=20L 1/4K 1/4 b.q=4L 1/10K 1/4 c.q=2L¹K² d.q=32 (L +2K)
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- A craft brewery hires 2 0 0 daily workers ( L ) at a wage ( w ) of $ 3 2 , and has 1 0 0 units of capital ( K ) at a rental rate ( r ) of $ 1 6 . If the brewery is minimizing costs, which of the following production functions would result in this hiring mix?Emco Company has an assembly line of fixed size A. Total hourly output is a function of the number of workers (crew size) as shown in the following schedule: Crew Size Total Output (No. of Workers) (No. of Units) 0 0 1 10 2 35 3 50 4 55 5 59 6 60 7 60 8 58 (a) Determine the marginal productivity of labor. (b) If the output is priced at $10/unit and the worker's wage is $40/hour, what is the optimal crew size?If the firm hires 5 employee, total fixed costs equals
- Do not use chatgpt. Thank you! production function 10Q = 1600L-4,800, where L is hired labour hours. If the wage rate that laborers receive is $10/hour, what is the cost function?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.A company is currently using its two inputs L and K, where MPL - 3.2K04L 02 and MPK - 1.6K -0.6 0.8 The firm pays a wage (W) of $80 per L and pays a rental rate of capital (R) of $40 per K. unit(s) of K for every The optimal (cost minimizing) combination of labor and capital is to employ unit of L (K should be times L). Answer as a whole number.
- (A) With P = 20, W = 25 and TFC = 500: Labor Output (Q) (L) 5 10 25 35 50 60 10 25 60 70 80 90 Marginal Physical Product of AVC=VC/Q ATC=TC/Q Labour (MPPL) 2 3 4 2 2 1 Average Physical Cost Product of (TC) (VC) Labour (APPL) 2 2.5 2.4 2 1.6 1.5 MPPL = Change in Q / Change in L APPL=Q/L TC = TFC + VC VC=W* L MC = Change in TC / Change in Q Total Variable Marginal Average Cost Variable 625 750 1125 1835 1750 2000 125 250 625 875 1250 1500 Cost (MC) 15 10 6 10 15 30 Average Total Cost Cost (AVC) (ATC) 12.50 10.00 10.42 12.50 15.63 16.62 62.5 30.00 18.75 26.21 21.88 22.22 Based on this table, answer this: 1. How much output will this firm produce? If the price of output increases to $30, how does your answer change? 2. If the productivity of labor increases by 10% (all else equal), how much more labor will the firm hire? 3. Below what price will this firm decide to produce zero units of output? (i.e. shut down)FarFlung make computer keyboards. They use both labour, L, and materials, M, in their production of keyboards. The production method they use requires that at least one labour and one material is always employed. FarFlung have a Cobb-Douglas technology which means that their production function is: Q(L, K) = LM. (a) FarFlung can make and sell 160000 computer keyboards. If fixed costs are £1000000 then what is the short run total cost of production and the short run average cost of production? (the price of labour is £100 and the price of materials is £25?) (b) FarFlung could move to a new factory, where they will be able to manufacture 360000 computer keyboards. They are confident they can sell all the keyboards, but they will need to reduce price from £20 to £10. Whilst they will be able to use the same technology, the fixed costs will increase to £2000000. i. What is the new level of short run average costs? What does this imply about the shape of the long run average cost curve?…A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is $4 and the rental rate on capital (r) is $5. Are the returns to scale increasing, constant, or decreasing for this production function? What cost minimization combination of K and L will the manufacturer employs to produce 300 units of output? Suppose that the price of capital increases to $7 per unit. If manufacturer continues to produce 300 units,what cost minimization choice of inputs capital and labor should the firm used. Suppose that the capital input is fixed at K = 3 units in the short run, what is the short run total cost function with q
- When the quantity of a variable input is increased from 3 units to 4 units the total output increases from 70 units to 85 units the marginal product of the variable input is 15 units? True/False1/3 7 Consider the production function y = (0.5/ +0.52 of producing 8 units of output per day. It pays a wage rate wi of $40 per hour and capital cost w2 of $10 per hour. How many units of labor and capital should the firm use? Suppose the firm wants to minimize the costA firm has the following information on production and costs from past data: Output (Y) 0 12 18 6 Total Cost (TC) 9 2775 5361 8199 If the total cost function is known to be TC = aY' + bY ² + kY + ƒ , and the demand for the product of the firm is Y = 320-(1/2). P answer the following: • 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.