Problem 3 Perfect Competition in a Rising Cost Industry Consider the food cart industry which is made up of identical rms with cost functions: 001} = 292 HF where pp is the price of a re extinguisher and q is the number of meals served. The demand for food cart meals is given by the unbelievable function: 123, me Dec) = (a) Derive the average cost function and show that the average cost increases as the price of re extinguishers increases. {13) Compute the break-even price for each rm in terms of pp. At the breakeven price, how much output does each rm produce (again, in terms of pp). (c) Suppose the price of re extinguishers is pp = 512. Find the equi- librium price of meals and number of rms. How many meals does each cart sell and how many meals are sold in the industry (total)? Time to make things a bit harder. Now, suppose that the supply of re ex- tinguishers is upward sloping. Specically, let's assume that the price of a re extinguisher is a function of the number of rms in the food cart industry: PF =3N2 We call this the inverse supply of extinguishers. So, for example, if there are ten food carts (N = 10), the price of a re extinguisher will be pp = 800 and so forth. (d) Find the long-run market supply. You can do this by following these steps: {i} Find the break-even price as a function of N. Find the output per rm at the breakeven price as a. function of N. (ii) Using your answer to (i), find the number of firms as a function of the price. (Hint: In the long-run, we know the market price will equal the break-even price.) (iii) Find the market supply as a function of price. (Hint: price again refers to the break-even price. The market supply is the number of firms times the output per firm.) (e) Using the demand and your answer to (d), find the long-run equi- librium market price (a specific number). How many firms are there and what is the price of a fire extinguisher? (f ) In words, explain why the long-run supply in this market is upward sloping. Do food cart firms earn positive profits in the long-run equilibrium