QUESTION 1 For the production function Qs = K0.6L0.5 in the short run, where capital is at 307 find the marginal product of labor at L = 68. 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).
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- 100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.a) SUPPOSE A FRIM PRODUCE OUTPUT USING THE PRODUCTION FUNCTION Q= 5KL .WAGE RATE FOR HIRING LABOR IS 200 AN HOUR AND COST OF USING CAPITAL IS 100 PER HOUR. FIND OUT THE OPTIMAL QUANTITIES OF LABOR(L*) AND CAPITAL(K*) TO PRODUCE 1000 UNITS OF OUTPUT? ALSO SHOW THE RESULT GRAPHICALLY AND INTERPRET .QUESTION 1 For the production function Qs = | K0.8 0.3 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).
- A farmer uses a certain technology that produces electricity. His production function is given as: q = f (k, l) = 1000k¹⁰/20 – 201³ Where q is the no. of megawatts of electricity his company is producing. Suppose that their electrical generators, k=20, calculate for the following: 1. Marginal product of labor 2. Average product of labor if k=20 3. If k decreases from 20 to 17, calculate the new MP of labor and the average product. Explain intuitively what happens to the MP and the average product.nestion # 1: (20) (a) Suppose a Firm produce output using the production function Q=5KL. Wage rate for hiring labor 200 an hour and cost of using capital is 100 per hour. (i) Find out the optimal quantities of labor (L') & capital (K’) to produce 1000 unit of output?. (ii) Also show the result graphically and interpret. (b) Explain the concept of Isoquant and Isocost line in firm theory. Mathematically derive the slope of isocost line and Isoquant and interpret.2-1 Consider the production function Y = X+4x2 – 0.2x3 a. Derive the exact marginal physical product and average physical product equations
- (1) q=35L + 40K (2) q=L.5K.5 a) For the production functions of (1) and (2) create the isoquants for q = 100, and for q = 144 with K on the vertical axis and L on the horizontal axis. (Use excel's scatter plot to draw these pictures. So, two pictures with two isoquants each.) b) Suppose that K is fixed at K = 9. Using excel draw the total product curves for equation (1). In a separate excel chart draw the marginal product and average product for K = 9 in equation (1). Give an explanation for the shapes of the total product, marginal product, and average product curve.A firm has a production function of ?(?,?) = ??.???.? a) Explain the concept of returns to scale. Does the function provide increasing, decreasing, or constant returns to scale? b) Provide an example of a typical sector with increasing returns to scale. c) Explain the concept of MRTS and argue whether the MRTS for this production function is diminishing. Please also provide a graphical illustration using numbers.Suppose the production function for widgets is given by KL – 0.5K2 – 0.1 L2 , where q represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labor input. (a). Suppose K=5; what is the average productivity of labor (Average product of Labor, MPL) (b). Suppose K=10; at what level of labor input does the total output reach the maximum?
- 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 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…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 988For the production function y = 2x1 + 3x2, What is the Technical Rate of Substitution? (Remember the negative sign.) Round your answer to two decimal places, e.g., -0.235 should be written as -0.24.
