Joe’s coffee house produces coffee drinks under the production function q = 5KL where q is the number of cups generated per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labor). What is the average product of labor(APL)? A. APL = 5 B. APL = 5K C. APL = 5L D. APL = 5K/L

Nia's Pizzas is a takeout-only pizza parlor servicing the college campus of Tallahassee that specializes in vegan pizzas. Nia's small shop has barely enough room for customers to stand and wait, let alone the five pizza ovens necessary to keep up with the hungry student customers. Nia signed a lease renting both the five ovens and the storefront for the next year. Due to the terms of the lease and the building's size constraint, Nia is unable to change the store's number of pizza ovens in the short run. However, Nia does face a decision regarding the number of employees to schedule on a weekly basis. Every Sunday, Nia contacts the staff to communicate the amount of workers needed on each day of the upcoming week. In the short run, the store employees are inputs, and pizza ovens are inputs. The following table presents Nia's daily production schedule. Fill in the blanks to complete the Marginal Product of Labor column for each worker. Output Marginal Product of Labor (Pizzas) Labor…

(2.2) Emily's coffee shop has a production function with L-shaped isoquants Capital (units) 12 8 4 3 6 q3=30 Labor (units) What's the optimal combination of capital and labor to efficiently produce q=30 units of coffee? 9 q2=25 q1=20

Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1 and the cost of a unit of capital is $3. The manager of this firm is interested in finding the following information: a)    Type of returns to scale and the marginal products of labor and capital. b)    The marginal rate of technical substitution of labor for capital. Graph the isoquant map. c)    The firm is currently producing 100 units of output. Find the optimal cost-minimizing quantities of labor and capital. Graphically illustrate this optimal solution using isoquants and isocost lines. What is the minimum total cost? d)    The manager now wants to know the K/L ratio to produce anyoutput level at the minimum total cost. Represent graphically the expansion path in the long run.

If a firm has 5 units of capital, 10 units of labor, and the production function is  Q = 4L + 3K what is the Marginal product of capital?   3 4 11 45

Suppose that a firm's production function is Q = F(L) = -1L³-30L² + 5,000L. Its marginal product of labor is MPL = -3L2-60L +5,000. a. At what amount of labor input are the firm's average and marginal product of labor equal (other than at L = 0)? Instructions: Enter your answer as a whole number. units. b. Confirm that the average and marginal product curves satisfy the relationship discussed in the text. When the amount of labor input is less than the quantity identified in your answer above, the marginal product of labor is greater than the average product of labor. When labor is greater than the amount identified above, the marginal product of labor is less than the average product of labor.

Suppose a firm has a Cobb Douglas production function and is initially producing 50 units of output using a long-run cost minimizing combination of inputs. The firm increases its output to 100 units. In the short run its level of capital remains fixed at the initial level (but the amount of labor used can be changed). In the long run, both inputs can change. On a graph, with amount of labor on one axis and amount of capital on the other, illustrate the expansion path in the long run and the short run. Draw an isocost line and an isoquant through each of the three solutions (i.e. before the increase in output, in the short run after the increase in output and in the long run after the increase in output. Note that both the second and third will be on the same isoquant). Your diagram does not need to be to scale, but should indicate the correct shapes and relative positions of the curves/lines.

PART 2 Question 1 a. The following table summarizes the short-run production functions for "All Needs Firms". The product of “All Needs Firm" sells for 5 GHC per unit, the cost of input X1 is 8 GHC per unit, and the price of input X2 is 25 GHC per unit. Complete the following table, and then answer the associated questions. Please show how you arrive at your answers. X1 X2 Q MPx1 APr1 AP2 1. 5 10 2 30 3 5 60 4 5 80 5 5 90 6 5 95 5 95 8 5 90 5 80 10 5 60 11 5 30 Answer the following questions using information from the above table. 1. Which input is the fixed input? Which is the variable input? 2. How much is the fixed costs? 3. What is the variable cost of producing 30 units of output? 4. Over what range of variable input usage does increasing marginal returns exist? 5. Over what range of variable input usage does decreasing marginal returns exist? 6. Over what range of variable input usage does negative marginal returns exists? b. You are the manager of a firm that sells output at a…

1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = «³K/3 + B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. | c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.

Suppose the production function for widgets is given by: Q = f (K, L) = 2 ∗ KL − K2/2 − L2/2 (a)  Suppose L=5 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and the average productivity of capital curve. (b)  At what level of capital input does the average productivity reach a maximum? How many widgets are produced at this point? (c)  Again, assuming L=5, derive an expression for and graph the MPK curve. At what level of capital input does MPK =0? (d)  Does this production function exhibit constant, increasing or decreasing returns to scale?