A company produces at most 15 (thousand) widgets per year. Its profit P, in thousands of dollars, is a function of n, the number of widgets prouduced per year( in thousands of widgets) the marginal profit is given by dp/dn = 20 + n -n^2. A. What is the marginal profit if n= 3 ( thousand widgets) should the company increase or decrease production B. What is the marginal profit of n= 8 ( thousand widgets) should the company increase or decrease production C. How many widgets should the compay proudcue in order to maximize

Is it true that if a firm’s technology exhibits the decreasing return to scale, then average production cost is increasing? (If yes, show the proof. If not, show a counter example)

Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (æ), the cost of a firm producing z items. An important microeconomics concept is the marginal cost, defined in (non- mathematical introductory) economics as the cost of producing one additional item. If the current production level is æ items with cost C (z), then the cost of computing h additionial (C(z+h)-C(z)) items is C (z + h). The average cost of those h items is . As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (z). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing z units of a certain item is given by C (z) = 0.02a3 – 10z + 450. (a) Find the marginal cost function. MC (z) (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50…

For its current level of production, a firm is attempting to minimize its costs. The firm has determined that the marginal product of labor is 10, the marginal product of capital is 20 and the cost per unit of labor is $5, whereas the cost per unit of capital is $10. To minimize cost for the given output the firm should   Increase the amount of capital and decrease the amount of labor Leave the amount of capital and labor as they are Decrease the amount of capital and increase the amount of labor