If a firm has the the production function F(K, L) = min(3K, 4L) What is its contingent demand for labor, Le(w, v, q)? q (a) 4w+3v (b) (c) 1/1 (d) 1/ (e) 9 when 9 3w+4v 4v and when w 4v
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- 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?0.8₁ A firm's production function is given by Q = 40K0.8L0.2 Each unit of capital costs $40 and each unit of labour costs $80. (a) Find the maximum level of output if the total input costs are $400,000. (b) Estimate the increase in production if an addtional $5,000 is made available. (c) Show that the ratio of marginal product to price is the same for both inputs. (a) Maximum output Q = (Round to the nearest integer as needed.)A firm's production function is given by Q = 40K0.8L0.2 Each unit of capital costs $40 and each unit of labour costs $80. (a) Find the maximum level of output if the total input costs are $400,000. (b) Estimate the increase in production if an addtional $5,000 is made available. (c) Show that the ratio of marginal product to price is the same for both inputs. (a) Maximum output Q = (Round to the nearest integer as needed.) (b) Increase in output is units (Round to the nearest unit as needed.) (c) The ratio of the marginal product of capital to price is (Round your answer to two decimal places.) The ratio of the marginal product of labour to price is (Round your answer to two decimal places.)
- E. A firm has the production function f(T1, 12) = 1750 , 50 What is the marginal rate of technical substitution (M RTS)? (a) MRTS =-1 2.5x, (b) MRTS = -x2/x1 (c) MRTS = -5x2/01 (d) MRTS =-0.5x2/21 (e) MRTS = -0.2x2/21 %3D %3D(2 ex Production function is flu, X2)=min (x,, 2-x) Dwhat are the conditional factor demand of y = 10 OVA the firm faces w, and w₂ as input prices, what is the cost function?1/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?
- Provethatthetechnologyf(L,K)=L2+K2 exhibitsincreasingreturnstoscale. What is the formula for the average product of capital? For the total cost curve TC(q) = q3, prove the technology exhibits decreasing returns to scale4) Please indicate whether the following production function has the characteristic of CRS, IRS and DRS. (b) F(K, L)=[aKe +(1-a)L¢ ]ve, (1>a>0, 1>p) 1. CRS 2. IRS 3. DRS 4. None of the aboveWhat is the maximum profit when the the profit-versus-production function is given below? P is profit and x is unit of production P = 200,000 – 1x- (1.1/(X+1)) to the 8th power?
- 2. A company's production output P is given in tons, and is a function of the number of workers N and the value of the equipment V, in units of $25, 000. The production function for the company is P(N,V) = 5N³/¼y/4. The company currently employs 80 workers, and has equipment worth $750, 000. (a) What are N and V in this case? (b) Find Py and Pv, then the values of P, PN, and Py at the values of N and V that you found in (a). (c) Give units and explain what each answer means in this context.dien There are two factors in a production function y = x 113 x₂¹1³. The market price of each unit ofy is p=3, and the factor prices are w₁=1 and W₂=2 for x₁ and X₂ respectively. variable (a). Calculate your cost function as a function of y if X, and x₂ are both barible factors. (b). Now derive the functions of average and marginal cost and plot them against quantity (C). Solve for your optional output of y. Calculate the ratio of two factors (X₁/X₂) (d). In the short run the fixed factor is set at X₂=1. What is the new optimal output level now?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.
