Suppose labour and capital are perfectly substitutable at a 2:1 rate, in such a way that 2 units of labor or 1 unit of capital can produce 2 units of output. What would be the equation for the production function? What is the average and marginal product of labor in this case?
From the given information , we get the equation:
Total product ,Q = L +2K
Average product , Q/L = (L+2K)/ L = 1+2K/L
Marginal product of labor , dQ/dL = 1
Suppose labour and capital are perfectly substitutable at a 2:1 rate, in such a way that 2 units of labor or 1 unit of c...
Suppose capital and labour are perfect substitutes in production for clothing: 2 units of capital or 2 units of labour produce 1 unit of clothing. Suppose capital and labour are perfect complements in production for food: 1 unit of capital and 1 unit of labour produce 1 unit of food. Suppose the economy has an endowment of 100 units of capital and 200 units of labour. Construct the production possibilities frontier for the economy.(Number the intercepts) What is the opportunity...
Problem #3: Long-Run Labor Dernand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which can be combined to produe Y units of output according to the following production function Y = 30K + 10L The firm wants to produce 600 units of output 1. Draw the ot that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and K on the vertical...
Please show all work.
Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which carn be combined to produce Y units of output according to the following production function: Y = 30K + 10L The firm wants to produce 600 units of output. 1. Draw the isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and...
A firm uses labour and capital to produce output according to the production function ??(??, ??) = 4??0.5??0.5, where L is the number of units of labour and K is the units of capital. The cost of labour is $40 a unit and the cost of capital is $10 a unit. a) On a graph, draw an isocost line for this firm, showing combinations of capital and labour that cost $400 and another isocost line showing combinations that cost $200....
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....
6. When a firm uses K units of capital and L units of labor, it can produce 2 units of output with the production function 2=VLEVK Each unit of capital costs 2, and each unit of labor costs 1. a. The level of K is fixed at 16 units. Suppose 234. What will the firm's short-run total cost be? (Hint: How much labor will the firm need?) b. The level of K is fixed at 16 units. Suppose 2 4....
A firm discovers that when it uses K units of capital and L units of labor, it is able to produce X = L^1/4*K^3/4 units of output. a. Draw the graph of isoquants in labor-capital plane. b. Suppose that the firm produces 24 units of output using 16 units of capital and 81 units of labor. Compute MRTS subscript LK. Compute the MPL. Compute the MPK. c. On the basis of your answer to part (b), is the equation MRTS...
Please show all work.
Problem #3: Long-Run Labor Demand and Factor Substitutability Suppose there are two inputs in the production function, labor (L) and capital (K), which carn be combined to produce Y units of output according to the following production function: Y = 30K + 10L The firm wants to produce 600 units of output. 1. Draw the isoquant that corresponds to that level of production (600 units) in a graph that has L on the horizontal axis and...
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
Assume that a firm has a fixed-proportions production function, in which one unit of output is produced using one worker and two units of capital. If the firm has an extra worker, say two workers, and no more capital, it still can produce only one unit of output. Similarly, an extra unit of capital does the firm no good.a) Draw the isoquants for this production function.b) Draw the total product, average product, and marginal product of labor curves (you will...