An economy has 22 units of labor and produces goods x and y. The production functions are x = 0.2L, and y = 0.5Ly, where Lx and Ly represent the labor allocation. Say the economy is currently producing x = 2 units and y = 6 units. This implies that Lx. and Ly= O 10; 14 O 10; 12 O 8:14 O 8; 12
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- Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?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.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.
- Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used () and the amount of capital used () by the following function: S- 20 L0 C0.7 In this formula L represents the units of labor input and Cthe units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. If your answer is zere, enter "p" Min 40 120 s.t. 20 S0000 (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial >oand C0 Do not round intermediate calculations. Round your answers to the nearest whole number 2991 2318 Cost S 397448 ide FeedbackWhat is the marginal physical productivity (MPP) of the inputs given the function Q = 12x + 2x1x2 + 2x²? Select one: O a. MPPT₁ 24x1 + 2x1 MPP₂ = 2x1 + 4x₁ O b. MPPT₁ = 24+ 2x₂ + 2 MPPT₂ = 2x1 + 4x2 OC. MPPT₁ MPPT2 O d. MPPT₁ MPPT - 24x₁ + 2x1 2x2 + 4x2 Time 24x₁ + 2x₂ 2x₁ + 4x2 Next pLet S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by the following function. S- 20100.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min s.t. -55,000 L.C20 (b) Solve the optimization problem you formulated in part (a). (Hnt: When using Excel Solver, start with an initial L>O and Co. Round your answers to the nearest integer.) at (L. C) =
- What is the marginal physical productivity (MPP) of the inputs given the function Q = 18z7 + 2x1#2 + 2x3? Select one: O a. MPP = 36x1 + 2x2 MPP, = 2x1 + 4x2 ОБ. МP, — 36+ 2г2 +2 MPP, = 2x1 + 4x2 %3D %3D O. MPP, 36x1 + 2x1 %3D MPP, = 2x1 + 4x1 %3D O d. MPP MPP, = 2x2 + 4x2 36z1 + 2x1 %3D %3DQuestion 1: Assume a firm wants to achieve an output level of 5400 units. This is the firm's production for that level of production: 5400 25K0.6 L0.4 Where Kis capital inputs and Lis labor inputs. Answer a) Yes or no, is this a level curve? b) what is dK2 dLQuestion 13 5 pts For the production function y = 4x1+ 3x2, which of the two inputs is more productive when x1 is 10 and x2 is 10? X1 X 2 neither; for this situation, they have equal marginal products cannot tell from the above information Question 14 5 pts Given the production function y = x1 1/3 x,1/3, what is the marginal physical product of x2 when x1 is 5 and x2 is 5? O 0.75 37 0.19 O 1.11
- 1) Suppose the prdduction function for widgets is given by: q= KL – 0.8K² – 0.2L?. a.) Suppose K=10, at what level of labor input does this AP1,reach a maximum and how many widgets are pIdduced at that point? At what level of labor input does MP1=0 and how many widgets are produced at that point? Graph the TP1, AP1 and MP1 curves. b.) Suppose capital inputs were increased to K=20. How would your answers to parts (a) change? c.) Does the widget production function exhibit constant, increasing, or decreasing retums to scale?(04.Suppose we are given (he constant returns to scale (CES) production function q= { ßa + aa }1/a a. Show that the marginal product of Beta is (g/B) and marginal product of Alpha (q/a)** b. Show that RTS = (2/B); I lence or otherwise shov that the ò =-1/(1-a) 1-a%3D For the production function y = 4x1 + 3x2, which of the two inputs is more productive when x1 is 4 and x2 is 2? O x1 O x2 neither; for this situation, they have equal marginal products cannot tell from the above information