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A19
Subject - economics
Consider a constant returns-to-scale production function f(k, l). Show that f(k, l) = k ∂f/ ∂k + l ∂f /∂l
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- Returns to scale in production: Do the following production functions exhibitincreasing, constant, or decreasing returns to scale in K and L? (Assume Ais some fxed positive number.)(a) Y = K1/2L1/2(b) Y = K2/3L2/3(c) Y = K1/3L1/2(d) Y = K + L(e) Y = K + K1/3L1/3 (f ) Y = K 1/3L2/3 + A (g) Y = K 1/3L2/3 − AProblem 1 Suppose firms have a CES production technology Y = [(AK)º + L°JË where -oa) An item is produced using two input factors. It is constant scale yield in production. The product is sold in a market with free competition ranse. One input factor is labor, the other is land. Demand for the item suddenly increases. Who will benefit the most from this the change: business owners, workers or landowners? NB! Here the answer is not obvious. You need to figure out how the answer is depends on the scarcity of resources, the substitutability between lom the input factors, whether there is competition in the commodity market, and short versus long term.a) An item is produced using two input factors. It is constant scale yield in production. The product is sold in a market with free competition ranse. One input factor is labor, the other is land. Demand for the item suddenly increases. Who will benefit the most from this the change: business owners, workers or landowners? NB! Here the answer is not obvious. You need to figure out how the answer is depends on the scarcity of resources, the substitutability between lom the input factors, whether there is competition in the commodity market, and short versus long term. b) An investor owns two companies. One company, A, produces aluminum minium. The other company, B, buys aluminum from A, paints this, and sells lacquered aluminum on to a world market with many competing companies. Company B pays company A a price q per kilo of aluminum. Company B sells lacquered aluminum for a price of per kilo. Company A's costs of producing x kilos of aluminum are given by the function: 1 СА (х) 3D X 2…Define returns to scale and its implications for production decisions.For firm A, is the following an internal or external economy of scale? Firm A benefits from a pool of trained labour in the area.1) In connection with the Law of the Minimum and the Law of Diminishing Returns, describe how the production function model can be a helpful tool in managing an agricultural production system.Which of the following equations does not represent a plausible production function? a.F(K,L) = 2KL b.F(K,L) = 2K-2L c.F(K,L) = 2(KL)0.5 d.F(K,L) = KLFor firm A, is the following an internal or external economy of scale? Firm A benefits from lower administration costs per unit as a result of opening a second factory.Confirm that the Cobb-Douglas production function satisfies all the three properties: more is better, concavity, and CRS.. From the standpoint of the final solution (amount of input used and the resulting amount of output produced): Group of answer choices A: Setting MRP = MFC is the same as setting MR = MC B: MR and MRP are always the same C: MC and MFC are always the same D: All other answers are correct10. Extension of the Cobb-Douglas Production Function-The Cobb-Douglas produc- tion function (Equation 7.16) can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form:" Q = y[@K* + (1 – a)L°]W/P where y is an efficiency parameter that shows the output resulting from given quantities of inputs; a is a distribution parameter (0 sas 1) that indicates the division of factor income between capital and labor; p is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the pro- duction process; and v is a scale parameter (v > 0) that indicates the type of re- turns to scale (increasing, constant, or decreasing). Show that when v = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of A, or K* = (A)K and L* = (1)L, and show that output Q also increases by a factor of A, or Q* = (A)(Q).]SEE MORE QUESTIONS
