### Production Function Analysis**2. A firm has a production function given by the following table:**| Units of Labor | 1 | 2 | 3 | 4 | 5 ||----------------|----|----|----|----|----|| **K = 1** | 3 | 8 | 12 | 15 | 17 || **K = 2** | 10 | 15 | 19 | 22 | 24 || **K = 3** | 16 | 21 | 25 | 28 | 30 || **K = 4** | 20 | 25 | 28 | 30 | 31 |**(i) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns?**To determine if the production function exhibits diminishing marginal returns when capital $ K $ is fixed at 2, we analyze the incremental output as units of labor $ L $ increase:- From $ L = 1 $ to $ L = 2 $: Output increases from 10 to 15 (Increment of 5)- From $ L = 2 $ to $ L = 3 $: Output increases from 15 to 19 (Increment of 4)- From $ L = 3 $ to $ L = 4 $: Output increases from 19 to 22 (Increment of 3)- From $ L = 4 $ to $ L = 5 $: Output increases from 22 to 24 (Increment of 2)The marginal output diminishes as labor increases, indicating diminishing marginal returns.**(ii) Does this production function exhibit constant returns to scale for all values of K and L?**To evaluate whether the production function exhibits constant returns to scale, we need to check if proportional increases in both $ K $ (capital) and $ L $ (labor) lead to proportional increases in output. Specifically, we compare the output when both inputs are doubled.Let's examine the data for the proportionality check:- When $ K = 2 $ and $ L = 2 $, output is 15.- When $ K = 4 $ and $ L = 4 $, output is 30.Doubling both $ K $ (from 2 to 4) and \( L

2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 15 K=2 K=3 K=4 20 25 28 30 31 (1) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L? 3 10 16 8 15 21 12 19 25 22 28 17 24 30

2. A firm has a production function given by the following table: Units of Labor 1 2 3 4 5 K=1 15 K=2 K=3 K=4 20 25 28 30 31 (1) Suppose that K is fixed at 2. Does this production function exhibit diminishing marginal returns? (ii) Does this production function exhibit constant returns to scale for all values of K and L? 3 10 16 8 15 21 12 19 25 22 28 17 24 30

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Consider the production function from earlier: Quantity of Haircuts 20 15 10 0+0 0 N 2 8 14 O Increasing marginal productivity O Constant marginal productivity O Decreasing marginal productivity 3 19 23 Labor (hours) 27 26 Total Product Curve From 1 labor hour up to 7 labor hours, what sort of marginal productivity does this production function have?
Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph TPL, APL, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (iii) the maximum value of MPL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…
Is each of the following statements true or false? In either case, briefly justify your answer. (a) If a firm has economies of scale, then its average cost is decreasing and lower than its marginal cost. (b) A firm whose total cost function is C(Q)=Q^2+Q must have economies of scale. (c) A firm with total cost function ?(Q) = 3Q+2 must have constant returns to scale. Plz do fast asap
13) A firm's total cost function is TC = 0.5Q², where Q is the output level. What is the returns to scale of the firm's production function? A) Increasing returns to scale. B) Decreasing returns to scale. C) Constant returns to scale. D) Negative returns. E) None of the above.
1. Given the production function: q = 2KL, (a) Fill in the table below which has information on the short-run production function, the marginal product of labor (MPL), and the average product of labor (APL) if capital is held fixed at 3 units in the short-run. Labor Quantity of Output (MPL) (APL) 0 1 4 9 16 25 (b) Plot the short-run production function. (c) Plot the marginal and average products of labor on a new graph. (d) Does the law of diminishing marginal returns apply? If so, at what level of labor do diminishing marginal returns set in? (e) What is the relationship between the marginal product of labor (MPL) and the average product of labor (APL)? (f) If the amount of capital increased to 6 units, what would happen to your graphs in part C)?
Which of the following production functions exhibit decreasing returns to scale? Select all that apply. O Q = 2K0.4 L0.6 O Q=0.5 K0.3 0.7 OQ=0.7 K0.4 L0.3 = K0.25 L 0.5 Q = 0.3 K0.5 L0.7 OQ=0.2 K0.3 L0.8
1. Figure 1 shows the production function of a firm. Y В Y2 Y1 X X1 X2 a) What are the variables along (i) of the X axis? (ii) Y axis? b) Does the firm operate in the short term or long term? c) Referring to the diagram above, what is the level of input where (i) firms experiencing increased marginal output? (i) does the firm experience a declining marginal output? (i) the firm achieves maximum marginal output? (iv) the firm achieves a blank marginal output?
For the production function Qs = K0.4L0.1 find the returns to scale, recall that a doubling of inputs that doulbes output is a CONSTANT returns to scale = 1.0 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
For its current level of production, a firm is attempting to minimize its costs. The firm has determined that the marginal product of labor is 10, the marginal product of capital is 20 and the cost per unit of labor is $5, whereas the cost per unit of capital is $10. To minimize cost for the given output the firm should Increase the amount of capital and decrease the amount of labor Leave the amount of capital and labor as they are Decrease the amount of capital and increase the amount of labor
a) Calculate the marginal product (MP1) for the mixers. Does the production function have increasing, decreasing, constant marginal product for the mixers? b) Suppose in the short run the amount of machines she has is fixed at 27. How many mixers should she use? How many baklavas will she produce? How much profit will she make? c)Usinag an isoprofit, as well as the production function, draw a diagram of your soltuion from part (b). carefully label all the slopes and intercepts. d) In the long run, how many mixers should she use? How many machines? How many baklavas will she make? e) Suppose that the government decides to provide a $1 subsidy per mixer. What is the profit-maximizing amount of input to use now?
7. The unit price of production input K is 8 euros and the unit price of production input L is 10 euros. What is the minimum cost at which a company could produce 20 units of product Y if the company's production function is Y = K / 4 + L?
30. The production function is f(L, M) = 4L1/2 M¹2, where L is the number of units of labor and M is the number of machines used. If the cost of labor is $49 per unit and the cost of machines is $16 per unit, then what is the total cost of producing 5 units of output?