If the price of labor is $5 and the price of capital is $10, what is the marginal rate of technical substitution at the optimal input choice?
0.5
2
decreasing
increasing
none of the above
at optimal input choice , marginal rate of technical substitution = price of labor / price of capital
In microe conomic theory, the Marginal Rate of Technical Substitution —or Technical Rate of Substitution —is the amount by which the quantity of one input has to be reduced when one extra unit of another input is used, so that output remains constant.
MRTS = PL / Pk = 5 / 10 = 0.5
If the price of labor is $5 and the price of capital is $10, what is...
Q=100K^0.7L^0.4 Find the marginal product of labor Find the marginal product of capital Is there diminishing marginal rate of technical substitution? Explain. Does the production function exhibit constant, increasing, or decreasing returns to scale.
At L=75, K=104, the marginal product of labor is 10 and the marginal product of capital is 22. What is the marginal rate of technical substitution (labor measured on the horizontal axis)? The marginal rate of technical substitution is nothing. (Enter a numeric response using a real number rounded up to two decimal places.)
Consider a firm that uses labor (L) and capital (K) to produce a general output (q) using the following production function: q = K0.8 L0.2 The firm seeks to produce q = 50 units for sale and faces prices for labor of w = 3 and capital of r = 5. a) What is the marginal rate of technical substitution? b) What are the optimal amounts of each input used by the firm? c) How much does the firm spend?
If labor and capital both exhibit increasing marginal products, then a production function cannot exhibit diminishing marginal rate of technical substitution of labor for capital. a. True b. False
For a particular combination of capital and labor we know that the marginal product of capital is 6 units of output and that the marginal rate of technical substitution is 3 units of capital per unit of labor. What is the marginal product of labor? Explain.
Problem 4: A firm has the following production function: Xi , X2)=X1 , X2 A) Does this firm's technology exhibit constant, increasing, or decreasing returns to scale? B) What is the firm's Technical Rate of Substitution? What is the optimality condition that determines the firm's optimal level of inputs? C) Is the marginal product of input 1 increasing, constant, or decreasing in x1. Is the marginal product of input 2 increasing, constant, or decreasing in x2? D) Suppose the firm...
Consider the case of a firm that produces output x (sold at price p) using a production function x = A*lαk1‐α‐βeβ, where l is labor, k is capital, and e is energy (for example, oil or electricity). a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale? Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Set up the profit maximization problem for the firm....
QUESTION 5 The marginal product for labor is given (MP) = 3 – 0.02*L; price of the product is $100 and wage = 200. Based on information above, the marginal product of labor at the optimal level of employment is $3 $2 $1.5 $1 2 points QUESTION 6 If the labor elasticity of output is 0.5 and the capital elasticity of output is 0.9, then the production function exhibits constant returns to scale. economies of scale. diseconomies of scale. diminishing...
3. Yasmin (Y) and Xavier (X) run firms that produce goods using capital (K) and labor (L). They each have technologies such that the Marginal Product of Capital is given by L (the amount of labor hired by the firm) and the Marginal Product of Labor is given by K (the amount of capital used by the firm). Thus, for Yasmin, the marginal rate of technical substitution for her firm is given by where the subscript indicates that this is...
#3
3. The isoquant map for a firm that produces output with labor and capital is shown on the next page. The price of labor is $20 per unit and the price of capital is $60 per unit. a) Draw the isocost lines for expenditures of TC =$300 and TC -$360. b) How many units of labor and how many units of capital should the firm hire to minimize the cost of producing Q. units of output? EXPLAIN. c) What...