Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1....

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1. Let ? be the amount of labor, ? the amount of capital, and ? be the amount of other materials used. Let the profit function be defined by ?=?−(??+??+??) where the costs of labor, capital, and other materials are, respectively, ?, ?, and ?.

Determine whether second order conditions for profit maximization hold, when the profit function is defined by ?=?−(30?+20?+10?) with ?=5?^0.3?^0.4?^0.2.

Solutions

Expert Solution

The second order derivatives of profit function with respect to capital and M will be negative less than zero which satisfies the profit maximisation conditions.

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider an economy with the following Cobb-Douglas production function:

Chapter 7, Labor Market Regulation (3 points):• Consider an economy with the following Cobb-Douglas production function:Y =k^1/3L^2/3The economy has 1,000 units of capital and a labor force of 1,000 workers.(a) Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock (Hint: Review Chapter 3.)(b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what are employment, output, and...

Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time,...

Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time, derive the conditional input demands ? ∗ (?, ?, ?) and ? ∗ (?, ?, ?) and the associated long-run cost function ?(?, ?, ?) under the assumption that ? + ? = 1. b) Describe the average cost and marginal cost functions. How do they depend on output q and factor prices w and r? Explain. c) Continuing to assume ? + ?...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l 1−α (a) Determine the relation between α and the marginal product of k and l. For what values of α is the marginal product for each input: (i) increasing, (ii) constant, and, (iii) decreasing. (b) Show that the marginal rate of technical substitution (MRTS) is equal to α 1 − α l k . For what values of α is MRTS decreasing in k?...

Consider the Cobb-Douglas production function Y = eb0 K b1 Lb2 eui where Y, K and...

Consider the Cobb-Douglas production function Y = eb0 K b1 Lb2 eui where Y, K and L denote real output, real capital input, and real labor input, respectively. The data for estimating the parameters of the production function are given in the Excel data file productionfunction.xls. Perform a logarithmic transformation of the production function to linearity so that it can be estimated by OLS. Compute the correlation coefficient between income lnK and lnL and comment on the potential for multicollinearity....

Question 1: Show that the Cobb-Douglas Production function Y = zKαN1−α, where 0 < α <...

Question 1: Show that the Cobb-Douglas Production function Y = zKαN1−α, where 0 < α < 1, satisfies all assumptions made in lecture 5. Assumptions: 1) Output increases when either the capital stock or the number of workers increase 2) Both the marginal product of capital and the marginal product of labor are decreasing 3) The marginal product of labor increases when capital increases, and the marginal product of capital increases when labor increases 4) For any constant x >...

Consider the following hypothetical economy. The production function is Cobb-Douglas and labor's share of income is...

Consider the following hypothetical economy. The production function is Cobb-Douglas and labor's share of income is 70%. All values are continuously compounded, annualized growth rates, in percent. Growth in real wages: 2.0 Growth in capital stock: 4.0 Growth in real rental rate of capital: 1.0 a. Using the information provided in the table above, your best estimate of growth in TFP is A. 1.4% B. 2.9% C. Not enough information to answer D. None of the above b. Consider a...

1. Consider the following Cobb-Douglas Production Function for Mauricio’s Machines Inc, a U.S. manufacturer of electronic...

1. Consider the following Cobb-Douglas Production Function for Mauricio’s Machines Inc, a U.S. manufacturer of electronic precision tools: Q = (L * 0.4) + (K * 0.7) a. Explain why a Cobb-Douglas production is indeed a representation of reality? b. Based on the function above, is Mauricio’s Machines’ business experiencing Economies of Scale or Diseconomies of Scale? Please explain your answer. c. If Mauricio’s Machines decided to boost Labor by 10% and Capital by 15%, how much would their productivity...

Stanford airline's production function is given by a Cobb-Douglas form: where: Y = number of passengers...

Stanford airline's production function is given by a Cobb-Douglas form: where: Y = number of passengers carried per year L = number of pilots (labor) K = number of aircraft (capital) a) show that the product elasticity for labor is given by EYL = a, and that the product elasticity for capital is given by /•'. ,.=/?. b) show that MPL > 0, MPK >0, and that tfY / âl: < 0 , &Y / cK2 < 0. c) show...

Consider a Cobb-Douglas production function: f(L, K) = 0.5K0.5L0.5. Using this production function, solve a short-run...

Consider a Cobb-Douglas production function: f(L, K) = 0.5K0.5L0.5. Using this production function, solve a short-run profit maximization problem for a fixed capital stock K=4, output price p=8, wage rate w=2, and capital rental rate r=4

1. The output of an economy is characterized by a Cobb-Douglas production function with constant return...

1. The output of an economy is characterized by a Cobb-Douglas production function with constant return to scale and an output elasticity with respect to capital equal to 0.3. Also given are the following parameters: 30% saving rate, 5% depreciation rate, 2% population growth rate, and the technology factor is 2. a). Find the capital-labour ratio, and also the output, consumption and investment on a per capita basis in the steady state equilibrium. b). Is a government policy that raises...

Subjects