Question

In: Math

The automobile assembly plant you manage has a Cobb-Douglas production function given by P = 30x0.5y0.5...

The automobile assembly plant you manage has a Cobb-Douglas production function given by

P = 30x0.5y0.5

where P is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget (in dollars). Assume that you maintain a constant work force of 120workers and wish to increase production in order to meet a demand that is increasing by 60 automobiles per year. The current demand is 800 automobiles per year. How fast should your daily operating budget be increasing? HINT [See Example 4.] (Round your answer to the nearest cent.)

Solutions

Expert Solution

Please UPVOTE if this answer helps you understand better.

Solution:-

Please UPVOTE if this answer helps you understand better.


Related Solutions

Suppose that you have a standard Solow model with production given by Cobb-Douglas function. Assume A...
Suppose that you have a standard Solow model with production given by Cobb-Douglas function. Assume A = 1, s = 0.1, α = 1/3, and δ = 0.1. Solve for the steady-state level of capital per worker, k* (Hint: use dynamic formula for capital stock.). Create an Excel spreadsheet to compute the dynamics of the capital stock. Plot the evolution of capital stock for 10 periods (i.e., t = 1, 2, … , 10) using your result in part (a)....
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...
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?...
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 ? + ?...
5. A Cobb-Douglas production function will yield a cost function that has constant Marginal Cost a....
5. A Cobb-Douglas production function will yield a cost function that has constant Marginal Cost a. True b. False ______ 6. The MC of a firm will intersect the ATC at the minimum point of MC a. True b. False _____ 7. For a cost-minimizing firm, it can continue to operate even if profits are negative. a. True b. False _____ 8. What cost concept do you use to determine whether a firm will shut down? a. Marginal Cost b....
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...
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...
Suppose a firm has a Cobb-Douglas production function. Show graphically that an increase in the rental...
Suppose a firm has a Cobb-Douglas production function. Show graphically that an increase in the rental rate of capital will increase the amount of labor hired if production remains at the same amount(10pts).
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 has the following Cobb-Douglas production function: Q = 2L0.5K0.5. The firms pays $50 for...
A firm has the following Cobb-Douglas production function: Q = 2L0.5K0.5. The firms pays $50 for each unit of labor (w) and $100 for each unit of capital (r). a. Consider a short-run problem where the firm's level of capital is fixed at 25 units. In this case, derive an exression that shows the optimal amount of labor (L) the firm would want to use in order to produce Q units of output. b. Use your answer for part (a)...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT