HOMEWORK 2: PERFECT COMPETITION IN THE SHORT RUN AND THE LONG RUN Suppose that the tin mining market is perfectly competitive. The market demand curve is given by D(P) = 300 P, where D is measured in units per year, and P is measured in $ per units. There are many potential entrants into this market, all of whom have identical cost curves. These cost curves are summarized in Table 1 below: Table 1 Cost Curve Formula Maginal cost (in $ per unit) MC = 30. Fixed cost per year FC = 100. (Annualized) Capital charge CC = 100. Capacity (in units per year) C = 20. The Deliverables Please complete each of the following tasks. While you do not need to show every graph and every step of algebra that you used to arrive at your answers, please show enough of your work so that I can gure out the logic that you used to arrive at your answer. Please keep your answer to three pages or less. Task 1: Draw in a graph the short-run supply curve of a single rm. Express as a function of Q the ATC and FR-ATC curve and draw them in a separate graph. Compute the minimum level of the ATC and FRATC curve and represent them graphically. Task 2: Suppose that the industry consists of 10 rms with cost curves given by those in Table 1. Find the short-run equilibrium price when the market consists of these 10 rms. (You should assume that these 10 rms act as price takers.) Task 3: Assume that there is large number of potential entrants with cost curves given by those in Table 1. Given this, what is the long-run equilibrium price in this market? At this price, how much does a typical rm supply? How many new entrants come into the market? What is the prot of a rm of at this equilibrium (taking into account the initial investment)? Task 4: As in Task 3, let's suppose that there are the same 10 incumbents, and a large number of potential entrants into this industry. However --- and here is the twist! --- suppose that the cost curves of these potential entrants, rather than being described by Table 1 above, have cost curves described by Table 2, but they have the same capacity constraint. (Keep in mind, the 10 incumbents have cost curves described by those in Table 1, so entrants differ from the incumbents.) Notice that the new entrants have higher MC than those of the 10 incumbent rms. You might imagine that the 10 incumbent rms have access to a scarce, superior resource (e.g., better veins of ore) that entrants do not have access to. If we continue to assume that the market demand curve is given by D(P) = 300 P, what is the long-run equilibrium price in this market? How much does each incumbent rm produce? How much does each entrant produce? How many entrants operate in the market? What is the prot of incumbent rms and new entrants at this equilibrium taking into account the initial investment? Table 2 Cost Curve Formula Maginal cost MC = 50. (Annualized) Fixed cost FC : 100. (Annualized) Capital charge CC:100. Task 5: Using your intuition, explain what would happen if, instead of Table 2, the cost structure of the entrants was given by Table 3. In particular, what would be the long term price and what would the reaction of the incumbent. Table 3 Cost Curve Formula Maginal cost MC = 10. (Annualized) Fixed cost PC = 100. (Annualized) Capital charge CC=100