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- What is the difference between a fixed input and a variable input?(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-aQ1 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.
- 1.) A firm engaged in the manufacture of RTWS faces the short-run production function Q = 250L - 5L², where L is the number of units of labor and Q is the number of RTWs produced annually. a.) How many units of labor are needed to maximize production output? b.) Find the maximum number of RTWs that can be produced by the firm in a year. c.) Compute the marginal product of the 10th unit of labor. d.) How many RTWS can be produced by the firm in a year if there are 10 units of labor? e.) Compute the marginal product of the 40th unit of labor. f.) How many RTWs can be produced by the firm in a year if there are 40 units of labor? g.) Sketch the graph of the production function.Problem 5 The production function of COVID vaccines for firm O is given by v° = VKL. and requires at least one unit of labor L and one unit of capital K, i.e. L>1 und K > 1. a) After a year and some thorough research, the production function changes to VO = V4KL. (I) Compute the marginal products with respect to labor L and capital K for both production functions ! (II) Which company's the marginal products is/are larger ? What happened to the original level of production after a year ? (III) Do the production functions exhibit increasing, constant or decreasing returns to scale ? b) Suppose now, we compare production functions of company O that discovered the vaccine to a second company M. The production function of M is given by VM = K0.6 L0.4 (I) Compute the marginal products with respect to labor L and capital K for this pro- duction function ! (II) If both companies used the same equal amount of labor L and capital K, which of them will generate more output ? (III) If the…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.
- Does the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?Lake Charles Seafood makes 500 wooden pack-ing boxes for fresh seafood per day, working in two 10-hourshifts. Due to increased demand, plant managers have decidedto operate three 8-hour shifts instead. The plant is now able toproduce 650 boxes per day.a) Calculate the company’s productivity before the change inwork rules and after the change.b) What is the percentage increase in productivity?c) If production is increased to 700 boxes per day, what is thenew productivity?2) The general Cobb-Douglas production function for two inputs is given by: q = f (k, l) = AKªL® where 0 0, f¡ > 0, frk 0. b.) Show that = a and ɛg,i Eq,k B (Note that ɛ's are elasticities). || C.) Show that, for this Cobb-Douglas function, production is CRS if a + ß = 1.