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2-1 Consider the production function Y = X+4x2 – 0.2x3 a. Derive the exact marginal physical product and average physical product equations
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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 988100VKL, 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.Explain the relationship between total product, marginal product, and averageproduct
- It costs a company $58 to produce 6 units of a product and $78 to produce 10 units. Assuming that the cost is linear, how much does it cost to produce 25 units?A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?From your knowledge of the relationships among the various production functions, complete the following table: Variable Input L Total Product QQ Average Product APLAPL Marginal Product MPLMPL 0 0 1 10 2 20 3 13.33 4 30 5 16.00 6 80 7 -10
- Suppose that the production function is given as follows:TPL = 10L + 5L2 + L3Find the total product, Marginal product and average product when L = 5.Dream Line manufacturing has a fixed scale of plant with the levels of total product given in the table below for different levels of labor. Complete the table by calculating the average product and marginal product. (0.5x8=4 Marks) Quantity of labor (workers) Total product Average product Marginal product 0 0 1 29 2 54 3 77 4 95nestion # 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.
- Only number 4b. Characterize the return of scale of production function cOn separate axes, draw typical production isoquants for each of the following production functions. a) f(x, y) = 2xy+1. c) f(x, y) = x + min{x,y}.Use the line drawing tool to plot the functional relation. listed below on a scale diagram (with X on the horizontal axis and Y on the vertical axis) and compute the slope of the line. Make sure you start at the Y-intercept and label the line 'Line A'. Y = 20 + 3X Carefully follow the instructions above, and only draw the required object.