13) You begin to work at a factory that produces Aguardiente (Firewater, a type of alcoholic beverage), the function of production its represented by the technology: Q(L, K, Z) = L³ K*z! Where with offers of input perfectly elastic A) Salary w is the price of labor L. B) Interest r is the price of capital K. C) Rent q is the price of drinkable alcohol Z. Calculate The function of demand for each input The function of offer for the Firewater The function of total costs for the Firewater The maximum benefit.
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- Consider a firm that produces output using industrial robots and skilled labor. Suppose it is the case that a reduction in the price of industrial robots causes the firm's labor demand curve for skilled workers to increase (i.e., to shift to the right). This implies that: There is diminishing marginal product of robots. O There is diminishing marginal product of skilled labor. O Robots and skilled labor are complements. O Robots and skilled labor are substitutes. The unit cost of skilled labor is below the unit cost of robots.1. Juan Valdez owns a coffee farm in Colombia. His production function is: f (x1, x2) = (x1 – 1)0.25 x9-5. Assume the price of input 1 is r and the price of input 2 is w.. (a) Write down an expression for the technical rate of substitution. (b) Find Juan's demand for inputs conditional on the quantity y of coffee Juan wants to produce. (c) Find Juan's cost function. (d) What is the supply function of Juan's firm? 2. Show that the profit function is convex in (p, w). 3. Find the profit function for the Cobb-Douglas production function f(¤1, 12) = Ax†' x" with A > 0, a1, ¤2 > 0 and a1 + a2 0, B > 0, 0 < a < 1, and 0 + p< 1. 6. Find the profit function for the CES production function. 7. Verify Hotelling's Lemma for the CES production function with B < 1.IV. Will can produce a higher grade, Gw, on an upcoming economic exam by studying. His production function depends on the number of hours he studies marginal analysis problems, A, and the number of hours he studies supply and demand problems, R. Specifically, Gw = 2.5A0.36R 0.64. His roommate David's grade production function is G) = 2.5A0.25R0.75 a. What is Will's marginal productivity from studying supply and demand problems? What is David's? b. What is Will's marginal rate of technical substitution between studying the two types of problems? What is David's?
- Consider a firm that produces a single output good Y with two input goods: labor (L) and capital (K). The firm has a technology described by the production function f : R? → R+ defined by f(1, k) = Vĩ + vk, where l is the quantity of labor and k is the quantity of capital. (a) In an appropriate diagram, illustrate the map of isoquants for the firm's production function. (b) Does the firm's technology satisfy the following properties: (i) strict monotonicity (i.e., are the marginal product of labor and the marginal product of capital strictly positive), (ii) the no-free-lunch property, (iii) constant/decreasing/increasing returns to scale? (iv) 1Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output ifit the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?Exercise 11 Question Help Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5KO.5/L0.5 - 0.5g/L 70- and MPK = 5L0.5/K.5 - 0.5g/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- -q= 280 q= 140 98 Suppose now that the firm wants to increase output to 280 units. If capital is fixed 0- in the short run, how much labor will the firm require? 70 84 L, Units of labor 14 28 42 56 112 The firm will now require units of labor. (Enter your response rounded to two decimal places.) K, Units of capital
- Question 4 The firm can use two inputs, L and K. The price of L= 20 and price of K = 30. Total cost = 300. As usual in the two input graph, units of L are on the horizontal axis and K on the vertical. The slope of the isocost line is [Select] The maximum units of K that can be purchased is [Select] The maximum units of L that can be purchased is [Select] 2 pts Is the bundle of K-9 and L- 5 on the isocost line? [Select]Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}. The inputs are perfect complement.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the long run total cost function, C(q)? Sketch it on the diagram.Suppose that labor is the only input used by a perfectly competitive firm.The firm's production function is as follows:a.Calculate the marginal product for each additional worker.b.Each unit of output sells for $10.Calculate the marginal product for each additional worker.cCompute the demand for schedule showing the number of workers hired.
- Suppose Mr. Saad is a producer of Lola Loo chocolate, following is the information available of his production plant. Quantity of Labour (L) Quantity of 1 2 3 4 5 Capital (K) 10 15 25 100 50 20 30 40 50 75 50 75 100 125 150200250 300 75 90 105 120 2 30 50 62 15 If K and Lare imperfect substitutes and complements from the information above draw at least three isoquant (map) and identify the level of production. H73 4Plz give answer ASAP. A price taking firm has the production function, q = f(l) = √ l where q is the output and l is the labor input. The price of labor input or wage is equal to $ 5, the output price is given by p, and the fixed cost is $80. a. Find the prices at which the firm makes a positive profit, and graph the prices along the curve, Hint find the profit function (SOLVE) b. Find the firm’s supply curve. (chek if correct) Q^2 = L TC or C(q) = wl = wq^2 The level of output wich firm maximizes profit is firms supply function We know profit function = pq – wq^2 dπ/dq = p – 2wq =0 p=2wq q(p,w) = p/2w thus supply function q=p/2w c. When p=10, since the firm makes a negative profit, it is better not to produce. True or False? Explain Hint part (a) we found positive values use (a) to demonstrate (SOLVE)Homework 2.1 Suppose a business manager of the factory wants to assess in terms of elasticity of demand, whetherthe products that his business is producing are complement goods or substitute goods inconsumption. So please explain which are the factors need to consider the long-run average cost curve in terms of usage of input?