Consider a firm that produces cars with the following production function: q = min(ak, bL) a. Find the Marginal Rate of Technical Substitution of labour for capital for this firm b. If per unit prices of capital (K) and labour (L) are r and w respectively, find the input demand functions for K and L; as well as the long run cost function c. Present your solutions graphically. (Thus, draw the Isoquant and Isocost of this firm)

Q: With a total cost function of: TC = 50 + 2Q +2Q², where Q is the output quantity, solve for the…

A: Total cost TC = 50 + 2Q + 2Q2 Fixed cost Fixed cost is that part of TC which does not depends on…

Q: The total cost function of a firm is given by: C = q(wy{v)! Where q is total output, W and V are…

A:

Q: A fast-food company in Hermanus has the following cost function: TC = 10 + 3K + 2L, where Lis the…

A: Given  total cost: TC=10+3K+2L            ......... (1) and production function Q=2KL       ........…

Q: Suppose the cost function is given by C(ω, υ, q) = qω^(1/3)υ^(2/3) (a) Use Shepard’s Lemma to find…

A: A)

Q: Given the average-cost function AC=Q^2-4Q+174, find the MC function. Is the given function more…

A: Average Cost (AC) function is given as:

Q: A firm faces the production function q = L²K³. Capital is fixed in the short-run at K = 1. Each unit…

A: q=14L2K3 Capital is fixed at K=1 Cost of labor=w Cost of capital=r

Q: A research study published in Social Science Medicine, “Production Functions for General Hospitals,”…

A: Given: Q = 5*Staff.34*Beds.64*Drugs.04*Specialists.02 Staff =20, Beds = 120, Drugs = 60, Specialists…

Q: Suppose that instead the production function now is F (L, K) = 0.2L + 0.7K. The wage rate (price…

A: Isoquant could be a curve that illustrates all the potential mixtures of 2 parts that make a given…

Q: Consider a production function of two inputs, labor and capital given by Q=LK. Let w =5 and r = 1,…

A: Production function refers to the function which shows the relationship between the final output and…

Q: The production function for Q is given as Q = 5K1/2L1/2where K is the amount of capital employed and…

A:

Q: Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to…

A: Marginal rate of technical substitution is the ratio of marginal product of labor and marginal…

Q: y= f(x1,x2)=x1ax2b Derive the equation for an isoquant curve.   If a=b=0.5 , the price of factor 1…

A: y = x1ax2b x2b = y / (x1a) x2 = [y / (x1a)](1/b)

Q: When production function  q= 0.2 LK+ 2L2K- 0.05L3K and  K= 10 are given, find amount of labor at the…

A: Given that: Production function:  q= 0.2 LK+ 2L2K- 0.05L3K K= 10 find the amount of labor at the…

Q: Suppose a firm with a production function given by Q = 30K0.5L0.5 produces 1,800 units of output.…

A: Firm minimizes cost by employing inputs at a point where ratio of marginal product of inputs is…

Q: Suppose a short-run production function is described as Q=30L-0.05L^2 Where L is the number of…

A: Given: Q=30L-0.05L^2 We know, MPL = dQ/dL Therefore, dQ/dL = 30 - L  So, MPL= 30-L = 0 L=30 units

Q: A firm's unit capital and labor costs are $1 and $2 respectively. If the production function is…

A: The maximum output of the production function can be determined by finding the marginal product of…

Q: Given prices for the two inputs as w1 = 1, w2 = 2, find the cost function of the (attached)…

A: Answer to the question is as follows:

Q: Question 1 The total cost function of a firm is given by: 2 C = q(W){cv) Where q is total output, W…

A: Note: Since a student has asked more than one question, we are going to ask the first question as…

Q: Consider the following production function: Q = 2K + 8L. Capital (K) is on the vertical axis and…

A: MRTS is the slope of isoquant. An isoquant shows all combination of L and K which yield the same…

Q: A widget manufacturer has a production function of the form q = L? K² . If the wage rate (w) is $4…

A: Since you have posted multiple parts questions, we will solve the first three parts for you. If you…

Q: When a firm uses K units of capital and L units of labor, it can produce Q units of output with the…

A: Production function measures the relationship between the units of output produced by using the…

Q: The short run production function is q = 10*L. The wage rate is $10 per unit of labor, then AVC:

A: AVC is total cost divided by output.

Q: Suppose the firm's production function is Q = 2KL, where Q is units of output, K is units of capital…

A: We can find out the short run production function using the capital K= 4.

Q: Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1…

A: The interplay between the output that a process gives and the various inputs that go in the process…

Q: The production function is y = min{x1 , x2} where x1 and x2 are the amounts of two inputs used. The…

A: Two goods are complements when they are consumed together in fixed proportion.

Q: Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to…

A: Cost is minimized at the point where ratio of marginal product of inputs is equal to price ratio of…

Q: Consider the following production function: Q= 2K + 8L. Capital (K) is on the vertical axis and…

A: MRTS refers to the rate at which capital can be substituted with labor by the firm.

Q: A firm has the following production function where q represents the output level per week, L…

A:

Q: Suppose a firm’s production function is q= 2L+ 5K, the wage is w= 4, and the rental rate of capital…

A: Cost function is the total cost incurred to produce a good. It is the total sum of cost incurred on…

Q: Suppose that the production of sports cars is given by the following production function: Q - (L/2+…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: The following table describes the various least cost combinations of two inputs from various…

A: Iso quant shows the different possibil combinations of inputs that give same level of output . And…

Q: Consider a producer with the production function y = min {2L, K} and suppose the input prices are…

A: Given, The production function, Y = min(2L, K), w = 1 r = 2 a) The cost function is given by: C = wL…

Q: Consider the Cobb-Douglas production function: 1. Derive the conditional input demands. 2. Derive…

A: Answer to  question 1 is:

Q: c) Give a formal definition of increasing, decreasing, and constant returns to sale, and determine…

A: Increasing Returns to Scale Increasing our inputs by m increases our output by more than m. Constant…

Q: A firm´s production function is given by: y = x² where y is the total output per time period, and x…

A:

Q: Consider a purely competitive firm that has two variable inputs L (labor hour) and K (machine) for…

A: We maximize the production function subject to the cost constraints. Cost=C=wL+rk Maximize:…

Q: Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100.…

A: We have Linear Isoquant, a*L+ b*K = QWhen L=0 and K = 10, Q = 100a(0) + b(10) = 100b = 10;Therefore,…

Q: Assume there is a linear isoquant where the input combination  K = 10, L = 0 produces Q = 100.…

A: We are going to find the production function first to check whether these two inputs are perfect…

Q: Assume that you have the following production function and input prices in the long run: 2 2 3 2 3 3…

A: Given: The production function and input prices are: W = 8 r = 4 Firm input bundle is (8, 10) To…

Q: A firm has a production function given by Q AL" K# and per unit prices of capital (K) and labour (L)…

A: given, Production function Q = ALαKβ                           Wages = w…

Q: A firm’s short-run production function is in the form of                        q = aLK +(bL^2)K…

A: Marginal production of labor (MPL) refers to the additional output that obtained by increasing one…

Q: A firm has the following production function, Q = Q(K,L) = K²+L², where Q is output, and K (capital)…

A: Firm gets maximum profit with use of  optimal level of input where the condition  Of MRTS = factor…

Q: Q.1.16 The vertical distance between the average total cost curve and the average variable cost…

A: Note: As per the guidelines, we are supposed to answer only one question when multiple questions are…

Q: Consider the production functions for X and Y given below. X = 2K2 + 4L ; Y = 10K0.5 L0.5 ; Suppose…

A: Production Function X = 2K2 + 4L ; Y = 10K0.5 L0.5