Can someone help me please please Cost minimization For the production fuction is given by f(l, k...
can someone help me please please Cost minimization For the production fuction is given by f(l, k) = √ l + √ k, where l is the quantity of labor and k is the quantity of capital, suppose that input prices are (w, r) >> 0, where w is the wage rate (price of a unit of labor) and r is the interest rate (price of a unit of capital). Suppose the firm must produce y > 0 units of output. (a) Formulate the firm’s cost minimization problem. (b) Illustrate the solution to the cost minimization problem in an appropriate diagram. (c) Solve the cost minimization problem to find the firm’s conditional input demand functions for labor and capital, and its cost function. (d) Assume that w = r = 4. In appropriate diagrams, illustrate the firm’s (i) conditional input demand for labor, (ii) its conditional input demand for capital, (iii) its total, average and marginal costs.
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Can someone help me please please Cost minimization For the production fuction is given by f(l, k...
Can someone help me please please Cost minimization For the production fuction is given by f(l, k...
can someone help me please please Cost minimization For the production fuction is given by f(l, k) = √ l + √ k, where l is the quantity of labor and k is the quantity of capital, suppose that input prices are (w, r) >> 0, where w is the wage rate (price of a unit of labor) and r is the interest rate (price of a unit of capital). Suppose the firm must produce y > 0 units of...
Production function: y= K^(1/2)L^(1/3) a) solve the cost minimization problem and find expressions for conditional labor...
Production function: y= K^(1/2)L^(1/3) a) solve the cost minimization problem and find expressions for conditional labor demand and conditional capital demand b)find the minimized cost function from a) c)suppose that w=r=1 and suppose that fixed costs are equal to FC=4. find and plot average fixed costs, average variable costs, average total cost and marginal cost
2. Consider the following cost minimization problem. A firm minimizes total cost given by, TC =...
2. Consider the following cost minimization problem. A firm minimizes total cost given by, TC = wL+rK subject to an output constraint as given by the production function, y=f(K,L)=8K05 +420S, where TC refers to total cost, L is labor input, K is capital input, r is the price of capital, w is the wage rate, and y is output. a. Derive the factor demand functions and the optimal cost function. The first order conditions and all the steps involved in...
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...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
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...
A firm has the production function F(L, K) = L1/2 + K1/2. The price of labor...
A firm has the production function F(L, K) = L1/2 + K1/2. The price of labor is $30 and the price of capital is $10. The firm has a production goal of 100 units of output. a) Carefully write out this firm’s cost minimization problem, using the particulars of this problem. b) Give two equations—particular to this problem—that the solution satisfies. c) Solve for the firm’s optimal input bundle. d) Determine the firm’s cost of producing 100 units of output....
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):=...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):=...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
Suppose labor (L) and capital (K) are fixed proportion inputs, and that each unit of output...
Suppose labor (L) and capital (K) are fixed proportion inputs, and that each unit of output must be produced with exactly 5 units of labor and 2 unit of capital. The price of a unit of labor is w, and the price of a unit of capital is r. a. Write down the production function. b. Derive the equation for the expansion path. c. Derive the equation for the long-run total cost function. d. Graphically depict the labor demand curve....
2. Consider the following cost minimization problem. A firm minimizes total cost given by, TC = wL+rK subject to an output constraint as given by the production function, y=f(K,L)=8K05 +420S, where TC refers to total cost, L is labor input, K is capital input, r is the price of capital, w is the wage rate, and y is output. a. Derive the factor demand functions and the optimal cost function. The first order conditions and all the steps involved in...
2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how...
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...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
Conditional/Unconditional demand for an input factor A firm produces an output using production function Q = F(L, K):= L1/2K1/3. The price of the output is $3, and the input factors are priced at pL 1 and pK-6 (a) Find the cost function (as a function of output Q). Then find the optimal amount of inputs i.e., L and K) to maximize the profit (b) Suppose w changes. F'ind the conditional labor deand funtionL.Px G) whene function L(PL.PK for Q is...
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