3. Suppose that a price-taking firm in the short run has total costs (including the fixed costs, even though they are sunk) given by: TC = 100 + 10Q +5Q2. a. (4 pts.) Suppose that p = 100. If the firm will produce a positive output, how much will it produce? Will it produce? (Explain how you know the latter.) b. (4 pts.) Suppose that p = 50. If the firm will produce a positive output, how much will it produce? Will it produce? (Explain how you know the latter.) C. (6 pts.) Now suppose that the fixed cost in the same) total cost equation is not sunk, i.e., can be recovered if the firm shuts down. Answer the same questions. 4. Departing from the standard model, suppose that marginal cost is constant. Suppose it is 50 $ per Q, meaning every additional unit that is produced adds 50 $ to cost (no matter what unit we are talking about). a. (3 pts.) What would be the equation of total variable costs in this case? (You can suppress units in all that follows.) b. (3 pts.) What is the equation of average variable costs in this case? C. (3 pts.)Graph marginal cost and average variable costs. (This is against Q of course, i.e., with Q on the horizontal axes.) d. (3 pts.) Now suppose the firm also has a fixed cost of say 100,000. Graph average total cost in this case continuing to assume constant marginal cost.)