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

The production function is Q = f (L, K0). Explain the total product, the average product and the marginal product, show the curves also graphically

Q = a,H + a,L +a,H² +a¸L² +a‚HL , where a,>0 2. Q = aH " L, where a, a, y> 0 a) Derive the equation of the relevant Isoquant. b) Find out whether the production function is well behaved.

Subpart 4

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)?

Consider the followng production function: 1 2 9 = x?x where x, and x, measure the employed quantities of input #1 and input #2, respectively. (a) Solve for and graph this firm's isoquant at q isoquant. 10. Please label three points along this (b) Does this production function exhibit increasing, decreasing, or constant returns to scale? Explain. Please corroborate your answer using a set of isoquants when the quantity of both imputs gets doubled. Note: Be sure to plot x2 along the y-axis.

What is the parameter in the production function in the following equation? F(K,N)=K N' ® OA. N O B. F OC. K OD. a

Subpart 1-3

Lesson 7- Production Question 8

Suppose the representative firm of the economy has a production function of the form F(K, N) = AKO.5N 0.5 The marginal product of labor is then given by MP N = 0.5AK0.5N –0.5 . The current capital 3. stock is K = 40. (a) Holding fixed capital at 40, draw a graph of output as a function of labor. What are some important features of this graph? (b) If A = 4 what is the Labor Demand Curve, ND(w), as a function of the real wage w? (c) Suppose labor is supplied inelastically with NS(w)= 10. What is the equilibrium wage w, employment level N, and full employment output Y ? (d) Suppose that productivity unexpectedly increases to A = 6. What is the new equilibrium wage w, employment level N, and full employment output Y ? (e) Depict this change graphically. Denote the original labor supply and demand curves by NS and ND respectively. Denote the new labor demand curve after the productivity shock by ND' . (Does not need to be to scale).