Suppose that the production function is given as follows: TPL = 10L + 5L2 + L3 Find the total product, Marginal product and average product when L = 5.
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Suppose that the production function is given as follows:
TPL = 10L + 5L2 + L3
Find the total product, Marginal product and average product when L = 5.
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- The amount of fish caught per week an a trawler is a function of the crew size assigned to operate the boat. Based on past data, consider the following production function identifying the relationship between output and labor input. You may assume that capital is fixed at 10 units.Labour Input (No of. Workers) (L) Total Product TPL (Q). From the table below :-(a) Calculate APL and MPL. (b) Graph APL and MPL. Do they have the expected shape? (c) On your graph, identify the three stages of production Labour input (No of Workers) (L) Total Product TP L (Q) 0 0 1 80 2 170 3 300 4 450 5 540 6 620 7 700 8 770 9 830 10 880 11 920 12 950 13 970 14 980 15 985 16 988 17 988Suppose 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 T PL, APL, and MPt. 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, (ii) the maximum value of M PL. (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…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…
- 2-1 Consider the production function Y = X+4x2 – 0.2x3 a. Derive the exact marginal physical product and average physical product equationsA production function is given by the following: F(L, K) = 5L2 + 4KiL %3D The production function exhibits: O Increasing returns to scale O Decreasing returns to scale O Constant returns to scale O Diminishing marginal product of laborExplain the relationship between total product, marginal product, and averageproduct
- Suppose a firm uses capital K and labor L to produce output Q with the following production function: 1 Q=4KL + = 1² 3 (a) Find the marginal product of capital and the marginal product of labor. (b) Find the average production of capital and the average production of labor. (c) Does this production function have increasing, constant, or decreasing returns to scale? Explain. (d) Find the marginal rate of technical substitution (RTS). (e) Use your result in (d) to find the elasticity of substitution. (f) Find the contingent demand functions for capital and labor if w is the price of labor input and v is the price of capital input.Cost curves Egidio Binaccio designed an ancestry app that allows people to connect with long lost Italian relatives. Egidio notices the following relationship between the number of hours he schedules and the number of downloads (sales) he gets. Below is a production function, for Egidios current company set up. NUMBER of LABOUR DOWNLOADS HOURS B) 10 C) 20 30 40 50 60 70 80 90 100 110 120 130 140 6.50 11.00 14.50 17.50 20.50 23.75 27.50 32.00 37.50 44.50 53.50 65.00 79.50 97.50 TVC TC MC AVC Suppose the firm can hire all the labour it would ever want at the going wage of $8 per labour-hour. The firm's total fixed costs are $64 per day. A) ATC Fill in the table showing total variable cost (TVC), total cost (TC), average variable cost (AVC), average total cost (ATC), and marginal cost (MC). [Remember: Marginal cost should be entered midway between rows of output.] On a graph with DOWNLOADS (per day) on the horizontal axis, draw the three "per-unit" cost curves, AVC, ATC, and MC. [Note…Determine the returns to scale for the following production functions. a) ? = K + 7L b) ? = KL3