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What is the production function if labor, L, and capital, K, are perfect substitutes and each...
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....
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. Wha...
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. What combination of labor and capital minimizes the cost of producing any output? To produce a given level of output q, how many units of L and K are needed? Express the optimal inputs choices L(q) and K(q) as functions of the level of output q
Assume a firm' production function is Q = 3K +L • In this case, inputs (K...
Assume a firm' production function is Q = 3K +L • In this case, inputs (K and L) are perfect substitutes. Can you give a real example where this production function works? Assume price of capital is r = 5, and price of labor is w = 1 How many units of capital and labor is need to produce Q=60 in cheapest way? O Show your logic using cost minimization condition, and Analyze it graphically
The production process used 2 inputs: Labor (L) and Capital (K). The production function is Q...
The production process used 2 inputs: Labor (L) and Capital (K). The production function is Q = min{2L,K} , the price of L is $3 and the price of K is $6. What's the minimum cost that the firm has to pay to produce 8 units?___
Specific Output Functions, Q = f(L,K): Below are some specific output functions. For each production function...
Specific Output Functions, Q = f(L,K): Below are some specific output functions. For each production function (1) Explain how the firm uses the inputs capital (K), and labor (L): (2) Provide an illustration of the corresponding isoquants the preference yield - include three isoquants with unique levels of output; (3) Provide a general form of the production function and create two specific production functions; and (4) Calculate the MRTS Lx for each of your proposed production functions (if possible). (1)...
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and...
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if f-0, the two input Labour and capital are imperfect substitutes in production
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if...
Suppose a firm can use either Capital (K) or Labor (L) in a production process. The...
Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firms Production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of Labor is $8 per unit. a) (4 points) What is the firm’s Total Cost function? TC(Q) = ____________________________ b) (8 points) Suppose the firm is producing 30 units of output (Q = 30). Using a graph, draw the firm’s isoquant for...
Suppose labor (L) and capital (K) are perfect substitute inputs. Each additional hour of labor increases...
Suppose labor (L) and capital (K) are perfect substitute inputs. Each additional hour of labor increases output by one unit, and each additional hour of capital increases production by 2 units. Workers are paid a wage rate (w) of $20/hour, and capital costs a rate of $50/hour. In the short-run, capital is fixed at 2. a. Mathematically derive and graphically depict Karen’s MPL and APL curves (on the same graph). b. Mathematically derive and graphically depict Aisling’s TC and VC...
a firm produces output according to the production function Q=4K+8L where K is capital and L...
a firm produces output according to the production function Q=4K+8L where K is capital and L is labour. in this production function are capital and labour (a) perfect complements (b) perfect substitutes (c) imperfect substitutes or (d) perfect substitues as long as labour is less than 8 and perfect complements when labour is more than 8.
Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, ...
Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $300 and each unit of capital costs $1,200. Further suppose a total of $120,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject...
Assume a firm' production function is Q = 3K +L • In this case, inputs (K and L) are perfect substitutes. Can you give a real example where this production function works? Assume price of capital is r = 5, and price of labor is w = 1 How many units of capital and labor is need to produce Q=60 in cheapest way? O Show your logic using cost minimization condition, and Analyze it graphically
Specific Output Functions, Q = f(L,K): Below are some specific output functions. For each production function (1) Explain how the firm uses the inputs capital (K), and labor (L): (2) Provide an illustration of the corresponding isoquants the preference yield - include three isoquants with unique levels of output; (3) Provide a general form of the production function and create two specific production functions; and (4) Calculate the MRTS Lx for each of your proposed production functions (if possible). (1)...
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if f-0, the two input Labour and capital are imperfect substitutes in production
Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if...
Suppose a Cobb-Douglas Production function is given by the following: where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this labor/capital combination. Suppose each unit of labor costs $300 and each unit of capital costs $1,200. Further suppose a total of $120,000 is available to be invested in labor and capital (combined). A) How many units of labor and capital should be "purchased" to maximize production subject...
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