5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5) (a) Setup and solve the...
5. Consider a firm with the production function F(K,L) = (K^3/5)(L^1/5)
(a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,r,q) and labor L*(w,r,q), and the long run minimized cost C* (w,r,q). (Hint: reduce the cost function for the next part.
(b) Setup and solve the profit maximization problem over quantity using the cost function you solved for in the previous part. Solve for the profit maximizing quantity q *(p,w,r), cost C*(p,w,r), and π *(p,w,r).
(c) Setup and solve the profit maximization problem over inputs. Solve for the profit maximizing amounts of capital K*(p,w,r), labor L* (p,w,r), output F(K ∗ ,L ∗ ), cost C*(p,w,r), and π*(p,w,r).
Homework Answers
Add Answer to:
5. Consider a firm with the production function F(K,L) =
(K^3/5)(L^1/5)
(a) Setup and solve the...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this form with both the two step and 1 step methods and provine that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K'(..) and labor L'(w. ), and the long run minimized cost C"(w.ne). (Hint: reduce...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
1. Suppose cars are produced using workers and machines as perfect complements. The production func- tion...
1. Suppose cars are produced using workers and machines as perfect complements. The production func- tion for producing cars is: F(K, L) = min(2K,5L) (a) Setup the short run cost minimization problem when K = 10. (2 points) (b) Solve for the short run optimal amount of labor Lsr() and short run minimized cost Csr(w,r,q). Circle your answer. (4 points) (c) Now suppose the car factory can freely choose capital (K) and labor (L). Setup the long run cost minimization...
4. Production of bikes requires 3 workers for every 2 machines, such that bikes are prodaced...
4. Production of bikes requires 3 workers for every 2 machines, such that bikes are prodaced according to F(K.L) min(3K, 2L) (a) Setup the short run cost minimization problem when R-6. (2 points) 5 (b) Solve for the short run optimal amount of labor Lsle) and short run minimized cost Csa(w,r.q). (3 points) (e) Now suppose the bike shop can freely choose capita! (K) and labor (L). Setup the long run cost minimiza- tion problem. (2 points) (d) Solve for...
1. The production function of a firm is f(1,k) = Vlk where l is labor and...
1. The production function of a firm is f(1,k) = Vlk where l is labor and k is capital/machinery. a. In the short run, if the quantity of capital is fixed at 64, derive the short run total cost SC(q), average cost SAC(q), and marginal cost SMC(q) of this firm. Assume each input costs $1 per unit. At what output does the minimum of SAC(q) occur? b. If labor and capital cost r and w respectively, and the quantity of...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital,...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm e...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
8.13. A firm produces a product with labor and capital. Its production function is described by...
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. Let w= 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q when the prices labor and capital are w = 1 and...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
5. Consider a firm with the production function F(K.L)= \/1/5 Tou will be solving the profit maximization for this form with both the two step and 1 step methods and provine that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K'(..) and labor L'(w. ), and the long run minimized cost C"(w.ne). (Hint: reduce...
3. Consider a firm with the production function F(KL)=1/31/3 You will be solving the profit maximization for this firm with both the two step and I step methods and proving that the final answers are identical. This big problem is broken up into the following smaller parts: (a) Setup and solve the long run cost minimization problem for the long run optimal amount of capital K*(w,,9) and labor L*(w,r.9), and the long run minimized cost C*(w, 5,9). (Hint: reduce the...
1. Suppose cars are produced using workers and machines as perfect complements. The production func- tion for producing cars is: F(K, L) = min(2K,5L) (a) Setup the short run cost minimization problem when K = 10. (2 points) (b) Solve for the short run optimal amount of labor Lsr() and short run minimized cost Csr(w,r,q). Circle your answer. (4 points) (c) Now suppose the car factory can freely choose capital (K) and labor (L). Setup the long run cost minimization...
4. Production of bikes requires 3 workers for every 2 machines, such that bikes are prodaced according to F(K.L) min(3K, 2L) (a) Setup the short run cost minimization problem when R-6. (2 points) 5 (b) Solve for the short run optimal amount of labor Lsle) and short run minimized cost Csa(w,r.q). (3 points) (e) Now suppose the bike shop can freely choose capita! (K) and labor (L). Setup the long run cost minimiza- tion problem. (2 points) (d) Solve for...
1. The production function of a firm is f(1,k) = Vlk where l is labor and k is capital/machinery. a. In the short run, if the quantity of capital is fixed at 64, derive the short run total cost SC(q), average cost SAC(q), and marginal cost SMC(q) of this firm. Assume each input costs $1 per unit. At what output does the minimum of SAC(q) occur? b. If labor and capital cost r and w respectively, and the quantity of...
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. Let w= 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm's long-run total cost curve as a function of quantity Q when the prices labor and capital are w = 1 and...
11. Consider the production function: f(K,L)=K+L. Let w and r denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function. (b) Find the profit maximizing output level and the profit function. 12. Consider a firm with production function f(K,L) = K +L. (a) Suppose that capital level is currently fixed at K = 10. Find the short term production cost function for...
Most questions answered within 3 hours.
-
3) What are the typical social structures in a global city?
asked 2 hours ago -
Luther Corporation
Consolidated Balance Sheet
December 31, 2019 and 2018 (in $ millions)
Assets
2019
2018...
asked 2 hours ago -
(Expected rate of return and risk) Carter Inc. is evaluating a
security. Calculate the investment’s expected...
asked 4 hours ago -
What specific indicators can point to lack of progress for
African Americans in American society?
asked 5 hours ago -
1-The Electrons in a beam are moving at 2.7×108 m/s in an
electric field of 15000...
asked 6 hours ago -
A gas tank is a vertical cylinder. It has a radius of 1m, a
height of...
asked 6 hours ago -
Accent Software faces the following conditions. All of these
support Accent’s use of a market-penetration pricing...
asked 7 hours ago -
A mathematically inclined friend emails you the following
instructions: "Meet me in the cafeteria the first...
asked 7 hours ago -
A monopoly sells in two countries . The demand curves in the two
countries are p1...
asked 8 hours ago -
A .15kg rubber ball is bounced off a wall. Before hitting the
wall, the ball moves...
asked 9 hours ago -
A manufacturing company preparing to build a new plant is
considering three potential locations for it....
asked 9 hours ago -
B. If compound Y has approximately the same values of solubility
in toluene as compound X,...
asked 9 hours ago