Production. Assume a production with two variable inputs (L, K). Show graphically the following and explain: a) fixed-proportions production function b) inputs are perfect substitutes
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- 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.The movement from point A to point B on the graph is caused by O a decrease in the price of the good. an increase in the price of the good. an advance in production technology. O a decrease in input prices. B P' P quaxtityWhich of the following is truc? (a) AFC + TO=ATC X (b) If total economic suiplus is negative due to a shift in a demand or supply curve, society is better 6ff (c) The law'of diminishing marginal refurns states that as the use, of an input increases, its MPP will never fall, instead will continue tò increase None of the above
- Question Establish input demand function in case of multiple variable inputsHow firm choose optimum combination of inputs in short run and long run explain theoritically and graphically?Refer to the graph below: y2 The graph above illustrates a production set of a firm. (a) Which assumption(s) do(es) the production set violates? Explain. (b) Suppose the firm decided to scale all inputs up or down by some amount t > 0. What will happen to the level of output?
- Answer 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?Problem 1 a) The local cleaner launders white clothes using the production function q = 3B + G, where B is the number of cups of a brand bleach and G is the number of cups of a generic bleach that is half as potent. a.1) In a graph, draw an isoquant. a.2) What are the marginal product of B and G? What is the marginal rate of technical substitution? TechnologyQ: Theoretically and graphically explain how firm choose optimum combination of inputs in short run and in the long run.
- 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) 1Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.