Imagine that the production function for tuna cans is given by q = 6K + 4L where q = Output of tuna cans per hour K = Capital input per hour L = Labor input per hour a. Assuming capital is fixed at K = 6, how much L is required to produce 60 tuna cans per hour? To produce 100 per hour? b. Now assume that capital input is fixed at K = 8; what L is required to produce 60 tuna cans per hour? To produce 100 per hour? c. Graph the q = 60 and q = 100 isoquants. Indicate the points found in part a and part b. What is the RTS along the isoquants?

Imagine that the production function for tuna cans is given by q = 6K + 4L where q = Output of tuna cans per hour K = Capital input per hour L = Labor input per hour a. Assuming capital is fixed at K = 6, how much L is required to produce 60 tuna cans per hour? To produce 100 per hour? b. Now assume that capital input is fixed at K = 8; what L is required to produce 60 tuna cans per hour? To produce 100 per hour? c. Graph the q = 60 and q = 100 isoquants. Indicate the points found in part a and part b. What is the RTS along the isoquants?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

See similar textbooks

Similar questions

What is the difference between a fixed input and a variable input?
Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a) Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b) At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c) Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d) Does this production function exhibit constant, increasing or decreasing returns to scale?
An electronics plant’s production function is Q = 5LK, where Q is its output rate, L is the amount of labor it uses per period of time and K is the amount of capital it uses per period of time. The Price of labor is $1 per unit of labor and the price of capital is $2 per unit of capital. a) What is the optimal combination of inputs the plant should use to produce 1000 units of output per period? b) Suppose that the price of labor increases to $2 per unit. What effect will this have on optimal L and K to produce Q=1000? c) Is this plant subject to decreasing returns to scale? Why or why not?
Frisbees are produced according to the production function q = 2K+Lwhere 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 isoquantd defined in part a and part b. What is the RTS along this isoquant? Explain why the RTS is the same at every point on the isoquant.
Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels:(Photo)Assuming that the price of labor (PL) is RO 2 and the price of capital (PK) is RO 3, calculate the total cost of production for each of the five levels of output using the optimal (least cost) technology at each level. How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? (Graph the total cost of production as a function of output. (put cost on the Y-axis). Which technology is the cheapest at all levels of output. Select one:a. None of the other three answersb. Technology Bc. Neither A Nor Bd. Technology A
Answer the given question with a proper explanation and step-by-step solution. Ned’s Tuna has the following production function: q = K3/4L1/4, Where q is the number of tunas per hour, L is the number of workers and K is the number of boats. Suppose that w = $20/hour (PL) and r = $30/hour (PK). a. Find Ned’s marginal product of labor (MPL). Does it exhibit diminishing marginal returns? b. Find Ned’s marginal product of capital (MPK). Does it exhibit diminishing marginal returns? c. Find and draw an isocost function for C
uppose a Cobb-Douglas Production function is given by the following:P(L,K)=60L^0.8K^0.2where LL is units of labor, KK 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 $900 and each unit of capital costs $3,600. Further suppose a total of $900,000 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 to your budgetary constraint?Units of labor, LL = Units of capital, KK = B) What is the maximum number of units of production under the given budgetary conditions? (Round your answer to the nearest whole unit.)Max production = units
Please only answer d Consider the following Cobb-Douglas production function: Y = 10 L^0.4 K^0.4. Suppose that the price of labor is w = 20 and the price of capital if r = 40. a- Derive the total cost curve for this production function. b- Derive the marginal cost curve for this production function. c- Plot the marginal and total cost curves for q = 1,2,3,4,5. What does it tell you about economies of scale for the production function? d- Suppose that the wage rate went up from 20 to 30. What would happen to the total wage bill relative to total costs wL/(wL+rK) What would happen to total costs?
Imagine that the production function for tuna cans is given by: q = 6K + 4L Where q = output of tuna cans per hour K = capital per hour L = labor input per hour. a. Assume capital is fixed at K = 6, how much L is required to produce 60 tuna cans per hour? b. Now assume capital is fixed at K = 8, how much L is required to produce 100 tuna cans per hour? c. Graph the q = 60 and q = 100 isoquants, in indicate the points found in parts a and b. d. What are the MP of capital and labor and What is the MRTS along the isoquants?
Using the information given in Table 5.2 (page 136), draw the isoquant correspond- ing to an output level of 20. Starting from L = 4 and K = 1, how much extra capital is needed to keep output constant if the labor is reduced by one unit to L = 3? How much extra capital is needed to keep output constant if the labor is reduced by one unit to L = 2 Table 5.2 Capital K L 1 2 3 4 5 6 1 10 14 17 20 22 24 2 14 20 24 28 32 35 3 17 24 30 35 39 42 4 20 28 35 40 45 49 5 22 32 39 45 50 55 6 24 35 42 49 55 60 Capital K is on the first column, and Labor L is on the first row.
Show using math and logic that for constant returns to scale production functions, MRTS between labor and capital depends only on the K/L ratio, and not the scale of production.
Suppose the production function for widgets is given byq = kl - 0.8k2 - 0.2l2where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input.a. Suppose k = 10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many widgets are produced at that point?b. Again assuming that k = 10, graph the MPl curve. At what level of labor input does MPl = 0?c. Suppose capital inputs were increased to k = 20. How would your answers to parts (a) and (b) change?d. Does the widget production function exhibit constant, increasing, or decreasing returns to scale?