2. A local business has asked an economic development consultant to help it decide if it can continue to compete with the other businesses in a city's downtown area in a very competitive market. Using historical data on costs, the consultant finds that the total cost function for this business is TC = 10 + Q + .1Q² where Q is amount of output this business produces. Given this TC function, we know that the marginal cost (MC) of production is P = 1+ .2Q. a. What are the fixed costs for this business? What is the business's variable cost function? What is the average total cost function? b. Calculate the level of output and the price of a unit of output in long run equilibrium. Sketch a graph of your solution (you do not need to precisely graph the ATC function, you just need to include a plausible version of it). c. Currently, the price of the product is $2.50 because of a recession that has hit the area. The consultant thinks the shop should immediately cease operations. Would you agree with this recommendation? Why or why not?

Given the following functions for shoe factory in Ohio: fi: Qa=2(90-P) 1 P==Qs 4 Where Q is quantity and P is price. fz given is the Marginal Cost for the shoe factory but this producer often dumps left over materials such as glues and dyes directly into the sewer effecting ground water in the nearby town. An expert in the field discovered that the marginal damage is a constant $9. 1. What is the social marginal cost (show all working)? 2. What is the new equilibrium when pollution damage is taken into consideration for this market? 3. What is the total surplus when accounting for the damages? (Evaluate at the SMC level) - Draw the diagram and label. 4. What is the Deadweight loss for the pollution in the event that the producers do not pay for the damages? (Identify the DWL on your diagram) 5. What is the Total Social Surplus taking damages into account?

A firm’s production is represented by the following function: Q = L1/4 K3/4 . The rental rate of capital (r) is $40 and the wage rate (w) is $12.a. For a given level of output, what should be the ratio of capital to labor in order to minimize costs?b. How much capital and labor should be used to produce 400 units of output? What is the total cost?c. What is the short run total cost if output is decreased to 300 units?d. How would the capital labor choice and total cost change in the long run?e. Would the firm prefer to relocate if input prices are r = 60 and w = 8 at an alternativelocation assuming relocation is costless?

Given the total cost equation: TC = 144 +2Q+Q² what is the average cost when the firm produces at the level of Q that yields the minimum average cost?

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…

Consider the following marginal cost function MC= 5 + 2qi. (a) Does the production process exhibits increasing returns? decreasing returns? constant returns? (b) If the price is $23. What’s the optimal production level? (c) If the price is $31. What’s the optimal production level?