Consider the following short-run production function (where L = variable input, Q = output): Q6L20.4L³ What is the marginal product function (MPL)? 12L - 1.2L² O 12 - 1.2L O6L-0.4L² What is the average product function (APL)? 12L - 1.2L² 6L-0.4L² O 12 - 1.2L What is the value of L that maximizes Q? What is the value of L at which the marginal product function takes on its maximum value? What is the value of L at which the average product function takes on its maximum value?

The short run production function of a competitive firm is given The short-run production function of a competitive firm is given by f (L) = 6L2/3, where L is the amount of labor it uses. (For those who do not know calculus—if total output is aLb, where a and b are constants, and where L is the amount of some factor of production, then the marginal product of L is given by the formula abLb−1.) The cost per unit of labor is w = 6 and the price per unit of output is p = 3. (a) Plot a few points on the graph of this firm’s production function and sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0, 12), the isoprofit line that passes through (0, 8), and the isoprofit line that passes through the point (0, 4). What is the slope of each of the isoprofit lines? (b) How many units of labor will the firm hire? (c) Suppose that the wage of labor falls to 4, and the price of output…

K Suppose that a firm's production function is q=5x in the short run, where there are fixed costs of $1,000, and x is the variable input whose cost is $625 per unit. What is the total cost of producing a level of output q? In other words, identify the total cost function C(q). The total cost of producing ya level of output q is A. C(q)= 1,000. OB. OC. OD. OE C(q)= 1,000+ C(q)= 1,000+ C(q) = 1,000+ 625q² C(q)= 25 q² 25 625q² 25 0.5 q B Dollars per unit of output 2000- 1800- 1600- 1400- 1200- 1000- 800- 600 400- 200- a 12 14 10 Quantity nchack 18 (1) Incorrect

In the short run, a firm which has production function f(L, M) = 4L1/2M1/2 must use 4 machines. If the cost of labor is £4 per unit and the cost of machines is £4 per unit, what is the short-run total cost of producing 48 units of output? Use Lagrange

Suppose that a firm has only one variable input, labor, and firm output is zero when labor is zero. When the firm hires 5 workers the firm produces 85 units of output. Fixed costs of production are $5 and the variable cost per unit of labor is $10. The marginal product of the sixth unit of labor is 4. Given this information, when the firm hires 6 workers the total output is amount to $ variable costs are $ production (rounded to the nearest cent) is cents. units, the fixed costs and the average total cost of

Fill in the missing data to solve this problem. Variable Total Average MarginalInput Product Product Product4      ?       70     ----5      ?      ?     406      350      ?        ? What is the total product for 5 units of input, and what is the marginal product for 6 units of input?