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 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. d) Graph the q = 50 and q = 200 isoquants for this production function also. Describe the shape of the entire isoquant map. e) Suppose technical progress resulted in the production function for

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 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. d) Graph the q = 50 and q = 200 isoquants for this production function also. Describe the shape of the entire isoquant map. e) Suppose technical progress resulted in the production function for

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.3P

See similar textbooks

Similar questions

What is a production function?
What is the difference between a fixed input and a variable input?
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.
Question 8 of 13 The following diagram depicts the production function of the farmers, where diminishing average product of labour is assumed. At A the average product of labour is 500,000/800 = 625 kg of grain per farmer. At B the average product of labour is 732,000/1,600 = 458 kg of grain per farmer. If you know that for 2,800 farmers the grain output is 894,000kg, then which of the following is/are correct? Kilogrammes of grain produced (thousands) 900 800- 700- 600- 500 400- 300- 200- 100- 0 0 400 800 B 1,200 1,600 Number of farmers 2,000 2,400 2,800 OA. The average product of labour when the labour input is 2,800 is 300. OB. The decreasing slopes of the rays from the origin to the production function along the curve indicate the decreasing average product of labour. OC. If the production function curve is an upward-sloping straight line, then there is no diminishing average product of labour. OD. It is possible that initially there is an economy of scale: for example, going from…
6. The Miller Company is trying to determine the combination of inputs to produce a specific volume of bar stools ordered. The production function for the firm is given: Q = 14LK? The wage of a worker is $80/day and the price of a machine is $240/day. If they need to produce 4,536 bar stools per day: a. What is the optimal combination of Labor and Capital, i.e. find the cost-minimizing combination of inputs to produce 4,536 bar stools? b. What is the total cost of using the inputs found in part a?
1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = «³K/3 + B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. | c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.
24. A specific production process can be represented by the production function, f(x1, x2) = (x 1/2 + x 1/3) 3. A. How much x₁ could the firm give up if it wanted to use 1 extra unit of x2 and still wanted to produce an identical level of output? B. Labeling everything and being precise, draw the isoquant corresponding to q = 4. = 9. C. On the same graph, draw the isoquant corresponding to q D. Between the isoquants you just drew, does the production technology display decreasing, increasing, or constant returns to scale? E. Analytically determine whether the production process has global returns to scale that match your local results from part D. Recall that in order to claim global returns to scale, your result must hold for ALL possible values of x1 and x2.
1. A firm can manufacture a product according to the production function Q = F(K,L) = K³/4L¹/4 a. Calculate the average product of labour, when the level of capital is fixed at 16 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 81 units of labour? b. Find an expression for the marginal product of labour when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labour depends on the amount of labour hired by calculating the marginal product of labour for 16 and 81 units of labour. c. Suppose capital is fixed at 16 units. If the firm can sell its output at a price of £100 per unit and can hire labour at £25 per unit, how many units of labour should the firm hire to maximise profits?
Table: Production Function for Soybeans Quantity of labor (workers) Quantity of soybeans (bushels) 1 25 45 3 60 4 70 75 Look at the table Production Function for Soybeans. Assume that the fixed input, capital, is 10 acres of land and a tractor, which have a combined cost of $150 per day. The cost of labor is $100 per worker per day. The total cost of producing 70 bushels of soybeans is: None of these options is correct. $1,024. $550. $250. $400.
5. The production function is given by y=x₁ + 2x2. If w₁ = 10, w₂ = 8, will the firm use input factor 2 to minimize the cost? In what case will the firm use input factor 2?
A firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is fixed. The quantity of Iron and the number of Cars produced is given by the following table: Tons of Iron per week Number of Cars per week 0 0 10 50 20 100 30 170 40 220 50 250 60 260 70 250 80 200 What is the average product of Iron when 40 tons are used? What is the marginal product of the 60th ton Iron? Does this production function exhibit diminishing marginal returns? If so, at what quantity of Iron do they start to occur?
Question B1 A firm produces a good, q according to the production function q = 2K0:2 L°0.8. The cost of a unit of labor is £5 and the cost of a unit of capital is £40. The firm is currently producing 160 units of output and has determined that the cost- minimizing quantities of labor and capital are 160 and 5 respectively. a. Graphically illustrate this situation on a graph using isoquants and isocost lines. Explain intuitively why there is such a difference between the capital input and labour input. b. The firm now wants to double output to 320 units. If capital is fixed in the short run, how much labor will the firm require? Illustrate this point on your graph and find the new cost associated with this level of labour and capital. c. Graphically illustrate how the cost-minimizing level of capital and labor will differ from your answers in a. d. If the marginal rate of technical substitution is 4K/L , find the optimal level of capital and labor required to produce the 320 units of…