Question

Directions: Please answer all items on this homework. This homework must be typed except for anything that needs to be graphed. No handwritten assignments will be accepted. You may do all graphing on a computer. But, realize you will not have a computer for the exam, so do not blindly trust the computer to do most of your work. You must show all your work. 1. How do you know if a production function is concave or convex? Please explain. (5 points) Please classify and explain what each stage of production you are in for each of the given scenarios: (5 points) 2. a. Average physical product is 45 and the marginal physical product is -60, b. Average physical product is 27 and the marginal physical product is 47, c. Average physical product is 46 and the marginal physical product is 26. 3. Please explain the relationship between average physical product (APP) and marginal physical product (MPP) (5 points) If your average physical product (APP) is equal to 3 using 5 inputs, what do you expect to happen to your current APP when your marginal physical product (MPP) is 9 when you move to 6 inputs? What is your new APP given this new MPP? Please show how you found 4. your answer. (5 points) Given that your total cost is $1,000,000, your total fixed cost is $200,000, and your output is 50,000, what are your a) total variable cost, b) average variable cost, c) average fixed cost, and d) average total cost? Please show how you found your answer. (5 points) 5. Suppose you have the following cost function c(y)- 16y + 200,000, please sketch the Average Fixed Cost, the Average Variable Cost, and the Average Total Cost curves wher represents the output and c(y) represents the total cost at output y. You may want to focus sketching these curves for outputs of 10, 20, 40, 50, 80, 100, 160, 200, 250, and 320. It is acceptable to sketch these curves using excel, but you should be able to sketch the curves by hand. (5 points) 6. e y Please explain the argument why marginal cost can equal both the change in total cost divided by the change in output and the change in total variable cost divided by the change in output when total cost and variable cost are not equal? (5 points) 7. 8. Please derive AVC- w/ APP, using the production and cost relationships. (Hint: define and apply the definition of AVC.) (5 points) Page 1 of 3 Last revised: 3/27/18

Answer 1

1) A production function, which has diminishing marginal product, is concave. Diminishing marginal product implies that when we move right along the production curve, sloe of curve decreases and this is property of concave function.

On the other hand, when marginal product increases, the production function is convex to origin.