4. Consider the following production functions: (i) Q = 4K2L2 (ii) Q = 2K + 4L...

4. Consider the following production functions: (i) Q = 4K2L2 (ii) Q = 2K + 4L (iii) Q = min(4K, 5L)

a. Graph an isoquant for Q = 400 for each of the production functions above.

b. In few words, explain what does the MRTS tell us about a production function?

c. Find the MRTS for production functions (i) and (ii).

d. Find the MRTS for production function (iii)

Solutions

Expert Solution

b) MRTS can be defined as amount of capital input that has to be given up to use an additional unit of labor so that output remains constant. MRTS is measured by the ratio of marginal product of labor and marginal product of capital.
Q = 4K² L² ( In this case production function is cobb douglus and iso-quant will be convex to orgin. This is due to dimnishing MRTS. )
Q = 2K + 4L ( In this case labour and capital are perfect substitutes which means inputs can be exchanged at a constant rate then Iso-quant will be a straight line. This is because MRTS will remain constant.
Q = min(4K, 5L) ( In this case labor and capital are perfect complements then iso-quant will be L-shaped. Inputs will be called perfect complement when both inputs must be used together in a fixed proportion.MRTS will be 0 or infinity because marginal product of each input will be zero.

Rahul Sunny answered 1 month ago

Next > < Previous

Related Solutions

Consider the following production functions: (i) ? = ?? + ??; (ii) ? = 1 2...

Consider the following production functions: (i) ? = ?? + ??; (ii) ? = 1 2 ? ?? ?; (iii) ? = 2? + 4? ?? ? + 3?? Variables ? and ? are positive parameters. a) Do the above production functions exhibit decreasing, constant, or decreasing returns to scale? Explain how your answer depends on parameters ? and ?. b) Using calculus, derive the marginal product of capital and labor for each of these production functions and then use...

3. Frisbees are produced according to the production function q = 2K+L where q =output of...

3. Frisbees are produced according to the production function q = 2K+L where q =output of frisbees per hour, K =capital input per hour, L =labor input per hour. a) If K = 10, how much L is needed to produce 100 frisbees per hour? b) If K = 25, how much L is needed to produce 100 frisbees per hour? c) Graph the q = 100 isoquant. Indicate the points on that isoquant deÖned in part a and part...

Consider the following statements: (I) A continuous functions is always differentiable. (II) The absolute value function...

Consider the following statements: (I) A continuous functions is always differentiable. (II) The absolute value function is differentiable everywhere. (III) If f(x) is differentiable everywhere, with f(−1) < 0, and f(2) > 0, then the equation f(x) = 0 must have a solution in the open interval (−1, 2). Which of the following is true? (a) Only (II) is always true. (b) Only (I) and (III) are always true. (c) Only (II) and (III) are always true. (d) Only (III)...

Exercise 3. Consider a firm with the Cobb-Douglas production function Q = 4L^1/3*K^1/2. Assume that the...

Exercise 3. Consider a firm with the Cobb-Douglas production function Q = 4L^1/3*K^1/2. Assume that the firm faces input prices of w = $7 per unit of labor, and r = $10 per unit of capital. a) Solve the firm’s cost minimization problem, to obtain the combination of inputs (labor and capital) that minimizes the firm’s cost of production a given amount of output, Q. b) Use your results form part (a) to find the firm’s cost function. This is...

Suppose a firm called, WeWorkTogether (Goal: profit maximization), has the following production function: Q = 2K...

Suppose a firm called, WeWorkTogether (Goal: profit maximization), has the following production function: Q = 2K 0.4 L 0.8. Q: units of output, K: units of capital, L: units of labor. If capital rents for $100 per unit per day, labor can be hired for $50 per unit per day, and the firm is minimizing costs, a. Find the long-run total cost of producing Q= 50 units b. Find the short-run total cost of producing Q= 50 units, when K is fixed...

QUESTION 3 A firm's production function is Q = 2 KL, with MP L = 2K...

QUESTION 3 A firm's production function is Q = 2 KL, with MP L = 2K and MP K = 2L. The wage rate is $4 per hour, and the rental rate of capital is $5 per hour. If the firm wishes to produce 100 units of output in the long run, how many units of K and L should it employ? a. K = 6.33; L = 7.91. b. K = 2; L = 2. c. K = 4;...

Q.4 Classify each of the following unemployment situations as either (i) structural; (ii) frictional, or (iii)...

Q.4 Classify each of the following unemployment situations as either (i) structural; (ii) frictional, or (iii) cyclical unemployment. Paul lost his job because his skills become obsolete. His employment counselor at the labor office advises him to retrain. Michael has just relocated to Seattle and he is now looking for a job. A data-entry employee loses his job because it was permanently outsourced to India. Unemployment increased during the Great Recession. Mary graduated from college with an economics degree. She...

Marginal costs of production are given by the following function: MC(Q) = 4 − Q Q...

Marginal costs of production are given by the following function: MC(Q) = 4 − Q Q ≤ 2 ,2Q − 2 Q > 2 (a) Plot the marginal cost curve. (b) Give the expressions for V C(Q) and AV C(Q). (c) Plot AV C(Q) on the plot from (a). (d) Give the expression for the supply curve of this firm. (e) Is it possible to find a different MC(Q) function that gives rise to the same supply curve? If yes,...

assume a firm has the production function q=k^1/4L^1/4, where k represents capital, L represents labor, r...

assume a firm has the production function q=k^1/4L^1/4, where k represents capital, L represents labor, r represents the price of capital and w represents the price of labor. Using the Lagrange method, derive the optimal quantities of k and l as a function of q,r,w

1. What do we mean by a "production function"? Interpret the following production functions. (a) Q...

1. What do we mean by a "production function"? Interpret the following production functions. (a) Q = 50L^3/4 K^1/4 (b) Q = 640K L^2-K^2L^3

Subjects