When labor increases from two to three workers, total product increases by Use the orange points (square symbol) to plot the production function on the following graph. Assume that if there are no workers, Underground Sandwiches does not have any output. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. BO 72 14 S 46 40 32 24 16 A 0 QUANTITY OF LABOR (Workers) per hour Production Function

Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used () and the amount of capital used () by the following function: S- 20 L0 C0.7 In this formula L represents the units of labor input and Cthe units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. If your answer is zere, enter "p" Min 40 120 s.t. 20 S0000 (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial >oand C0 Do not round intermediate calculations. Round your answers to the nearest whole number 2991 2318 Cost S 397448 ide Feedback

A custom motorcycle company can produce more motorcycles if it has more workers. The company has experimented with hiring workers in teams of four and has come up with the following table relating the number of workers to the companies annual production Part1. Using the straight line tool, graph the production function based on the information given. Construct the curve using four line segments joined end to end. Don it graph the individual points. Part 2. Give the numeric answers to tap decimals. A. The marginal product of each of the first four workers is ______ B. The marginal product of each of the second four workers is _______ C. Diminishing returns begin with the _______ worker.

Underground Sandwiches, a sandwich shop, has the following marginal product curve (labeled MP) for its hourly production. MARGINAL PRODUCT (Sandwiches per worker) 80 72 64 56 48 40 32 24 m 16 B When labor increases from three to four workers, total product increases by 00 18 8 16 Use the orange points (square symbol) to plot the production function on the following graph. Assume that if there are no workers, Underground Sandwiches does not have any output. 0 12 Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. 9 m 2 0 0 O 2 3 LABOR (Workers) 0 O MP QUANTITY OF LABOR (Workers) 5 per hour. Production Function

Suppose the production function for widgets is given by q=kl -0.8k²-0.21² where q represents the annual quantity of widgets produced, k represents annual capital input, and I represents annual labor input. Suppose k = 10; at what level of labor input does this average productivity reach maximum? (please put your answer in numerical values with no comma or decimal place). How many widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 10, at what level of labor input does MPL = 0? Suppose capital inputs were increased to k = 20, at what level of labor input does this average productivity reach maximum? widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 20, at what level of labor input does MPL = 0? answer in numerical values with no comma or decimal place). Does the widget production function exhibit constant, increasing, or decreasing returns to scale?…

please show graphs and table thank you

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?

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Consider the production function from earlier: Quantity of Haircuts 20 15 10 0+0 0 N 2 8 14 O Increasing marginal productivity O Constant marginal productivity O Decreasing marginal productivity 3 19 23 Labor (hours) 27 26 Total Product Curve From 1 labor hour up to 7 labor hours, what sort of marginal productivity does this production function have?

The following equations represent the long-run production functions for four different technologies, where capital and labor are both variable inputs. For each function, indicate whether it exhibits increasing, decreasing, or constant returns to scale. Clearly show your derivations. (Note that in parts a and c, the exponents are decimals.) f(L,K)= 8L²K4 b. f(L,K)= L+7K c. f(L,K)= L³K d. f(L,K)= 4L+K? а. с.