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- What is the elasticity of substitution of f(K, L) = KL²? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1 (e) 3/2 (f) 2 Which of the following represents increasing returns to scale? (a) f(K, L) = (K² + L²)¹/2 (b) f(K, L) = (K¹/2 + [¹/2)² (c) f(K, L) = (K + L) (d) f(K, L) = (K + L)² Suppose the production function for good q is given by q = (k¹/2+1¹/2)2. Consider the following three statements about this function: I. The function exhibits constant returns to scale. II. The function exhibits diminishing marginal productivities in both inputs. III. The function has a constant rate of technical substitution. Which of these statements is true? (a) All of them (b) None of them (c) I and II, but not III (d) II and III, but not I*Find the elasticity of scale and the elasticity of substitution for the CES production function f(x1,x2) = (x{ + x%)¯,where 0 #p<1.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) Suppose a company has this Leontief production function Q = min(20K,50L) i) List a few combinations that will produce 500 units of outputQ1 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.E. A firm has the production function f(T1, 12) = 1750 , 50 What is the marginal rate of technical substitution (M RTS)? (a) MRTS =-1 2.5x, (b) MRTS = -x2/x1 (c) MRTS = -5x2/01 (d) MRTS =-0.5x2/21 (e) MRTS = -0.2x2/21 %3D %3D
- : Suppose that the production functions be like as (A) i) Y = X15 X20.5 ii)Y= X10.5 + X20.5 Find MRTS of these functionsFind the elasticity of scale and the elasticity of substitution for the CES production function (x1; x2) = (x1rho + x2tho 1/P, where 0 * p > !!!The production function is f(L,K)= L2/3K 1/3 , where L is the amount of labor and K is the amount of capital. (a. Find the marginal products of labor and capital. Is the marginal product of labor diminishing, increasing or constant in labor? (b. Sketch several isoquants in the K-L space. (c. Find the Technical Rate of Substitution between capital and labor. (d. What are the returns to scale of this production function? Please explain it with details
- The production function is f(L,K)= L2/3K 1/3 , where L is the amount of labor and K is the amount of capital. (a. Find the marginal products of labor and capital. Is the marginal product of labor diminishing, increasing or constant in labor? (b. Sketch several isoquants in the K-L space. (c. Find the Technical Rate of Substitution between capital and labor. (d. What are the returns to scale of this production function?A factory makes bicycle tires. The cost, C, in dollars and revenuue in dollars, R, are both functions of the number of tires, n.a) Describe what is meant by C'(4) = 8b) Generate a mathematical equation, using function notation, to model the following statements: for (b) + (c) "The marginal revune for 15 tires sold decreases by $1."c) "The revenue at 3 tires equals the change in cost at 5 tires"(v) Find the ratio of the marginal productivities of two inputs, at L=2 and K =3 when the production function is given by Q= 8LK- L2 -K?