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

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Rahul Sunny answered 2 years ago

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 a firm whose technology can be represented by the following Cobb-Douglas production function: , f(L,K)...

Consider a firm whose technology can be represented by the following Cobb-Douglas production function: , f(L,K) = L0.5K0.5, where L and K represent labor and capital, respectively. In a new diagram, in please draw an isoquant that represent an output level of 20 units. Suppose the price of labor, w, is 1 and the price of capital, r, is 2, and the firm’s budget, C, is 100. Please draw the firm’s isocost line in the same diagram. Can the firm...

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...

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....

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 ? + ?...

Given the following Cobb-Douglas production functions: F(L,K) = LK^2 F(L,K) = L^3/4K^1/4 F(L,K) = L^1/2K^1/4 1....

Given the following Cobb-Douglas production functions: F(L,K) = LK^2 F(L,K) = L^3/4K^1/4 F(L,K) = L^1/2K^1/4 1. Determine the returns to scale for each function. 2. For the rest of this exercise assume that the price of labor, w, and the price of capital, r, equal 1: w = r = 1. Find the conditional input demand functions of labor and capital (the cost-minimizing combinations of labor and capital). 3. Now find the cost functions for each of the production functions....

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.

A firm production is represented by the following Cobb-Douglas function: Q = K^1/5 L^4/5. The rental...

A firm production is represented by the following Cobb-Douglas function: Q = K^1/5 L^4/5. The rental rate, r, of capital is given by $240 and the wage rate is $30. a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs? b. How much capital and labor should be used to produce 400 units? How much is the total cost? c. What is the short run total cost if output...

Consider the production function F(L,K) = L^2/3 K^2/3 . (f) Does this production function exhibit increasing,...

Consider the production function F(L,K) = L^2/3 K^2/3 . (f) Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. (g) Find the total cost, average cost and marginal cost of producing y units of output. Is the average cost increasing or decreasing in y? Is the marginal cost higher or lower than the average cost? Question 2 The production of magic chairs requires only two inputs: seats (S) and legs (L) (no other inputs are required...

Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the...

Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the number of machines), L is labor (the number of workers), and H is human capital (the number of college degrees among workers). Markets for output and factors of production are both competitive. The production function is Y = K^1/3*L^1/3*H^1/3 1. Prove that this technology shows constant returns to scale. 2. Solve the competitive firm’s profit maximization problem by deriving the first-order conditions. 3. An...

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