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What is the value of the bordered Hessian determinant of the generalized Cobb-Douglas production function
q=K^0.3L^0.5
subject to 2K+L=120?
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- What is the value of the bordered Hessian determinant of the generalized Cobb-Douglas production function q=K0,3L0,5 subject to 2K+L=120?What is the value of the bordered Hessian determinant of the generalized Cobb-Douglas production function q=K0.3 L0.5 subject to 2K+L=120 ? A) K0,5/L1.5 + 0,6/K0,7L0,5 + 21L0,5/K1,7 B) 21L0.5/K1,7 + K0,7/L0,5 + 1/K0,3L1,5 C) K0.3/L1,5 + 0,6/K0,7L0,5 + 21L0,5/K1,7 D) K1,7/L1,5 + 21/K0,7L0,5 + 1/K0,3L1,5Take a Cobb-Douglas production function, find its Elasticities w.r.t output and Elasticity of Substitution with the help of partial derivatives.
- A widget manufacturer has an infinitely substitutable production function of the form q= 2K+L a. Graph the isoquant maps for q=20, q=40, and q=60. What is the RTS along these isoquants? b. If the wage rate (w) is $1 and the rental rate on capital (v) is $1, what cost-minimizing combination of K and L will the manufacturer employ for the three different production levels in part a? What is the manufacturer’s expansion path? c. How would your answer to part b change if (v) rose to $3 with (w) remaining at $1?If the production function is F(K,L)=A∗K0.4L0.6 then the marginal rate of technical subsitution isConsider the following production function:q = (KL)^α, where α > 0. (a) Confirm that the marginal physical product of capital is homogenous of degree zero in the case in which the production function exhibits constant returns to scale.(b) Derive an expression for the cost function of a firm using the production function to produce output of a good.(c) Find the first and second partial derivatives of the cost function with respect to q. Interpret the second partial derivative and relate the sign of the derivative to the returns to scale.
- Answer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.For the production function q = f(K, L) the ratio of the percentage change on K/L with percentage change on PK/PL is called elasticity of substitution. Write down a constant returns to scale Cobb-Douglas production function and find its elasticity of substitution for the K = 10, L = 7, PK = 4 and PL = 3 levels.The Cobb-Douglas production function can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: Q=γ[δK−ρ+(1 - δ)L−ρ]−ν/ρ�=�[δK−ρ+(1 - δ)�−ρ]−ν/ρ where γ is an efficiency parameter that shows the output resulting from given quantities of inputs; δ is a distribution parameter (0 ≤ δ ≤ 1) that indicates the division of factor income between capital and labor; ρ is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and ν is a scale parameter (ν > 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Complete the following derivation to show that when ν = 1, this function exhibits constant returns to scale. First of all, if ν = 1: Q� = = γ[δK−ρ+(1 - δ)L−ρ]−1/ρ�[δK−ρ+(1 - δ)�−ρ]−1/ρ = = γ[δK−ρ(−1/ρ)+(1 - δ)L−ρ(−1/ρ)]�[δK−ρ(−1/ρ)+(1 - δ)�−ρ(−1/ρ)] = = Then, increase the…
- Given the Production function for Mwaba & Mutale Enterprises as follows: Q = f (k,l) = 300k 2l2 - k 3l3, Assuming the value of K is 5, Determine the value of L, for which APL is maximum Prove that at the point where MPL is equal to APL , APL is maximum. The value of labor input L, for which output is maximum Total output at this value of labourSuppose the input combination currently used by a producer is such that the TRS is equal (in absolute value) to the ratio of the input prices. Then, we can conclude that the producer is maximizing her profits. Group of answer choices True FalseDo the following production functions exhibit increasing, constant, or decreasing returns to scale? Provide calculations supporting your answers.