1 Partial equilibrium analysis Suppose is a market currently having 2, rms. The market demand information is given by p = 550 5%. Again, Q is the total output in the market. Each rm has the following eest function em = an + {12 1.1 Explain how you knew that this is a shortrun er longrun cost function. Find the shortrun protmaximising quantity of output for each rm in this market, and the prot for each rm. 1.2 Now, let's consider the longrun adjustments that may occur in the market. As discussed in clam, long-run adjustments typically take the form of the rms adjusting their inputs and the size of their xed costs, and rms entering or exiting the market. But for simplicity, here we amunie that the xed input is a license, and you can cheese either El quantity of the license [meaning that you cannot sell any output in the market] or 1 quantity (at cost d giving you the right to sell in the market}. Consequently, all of the long run adjustments take the form of rms entering or existing the market. The long run cost fimction is thus given by the following 4IIIIl+a2 if grail C = is} {a if q= 1i.ui'ii'hat is the longrun prot for each rm? 1i.a'ii'hat is the long run market price and quantity of output produced by each rm? What is the longrun number of rms in this market? 1.3 Suppose that production process used in the market causes pollution. There is a technology that will eliminate this pollution. To do so, it requirm the install ment of a device. The cost of this device is 225 per rm, which is independent 1 of the quantity produced by the firm. Assume that the market is initially in the long run equilibrium that you just found in 1.2. Assume that now each firm in this market is required to install this device. Write the new cost function for a firm in this market. Find the short-run putput level and profit for each firm, and the price. Then, find the long run quantity of output per firm, market price, and profit. Who would bear the cost of pollution technology? 1.4 Suppose there is another technology to eliminate the pollution. For this technol- ogy, the cost depends on the quantity of output the firm produces, and imposes a cost of 11.25 per output produced. At the equilibrium calculated in 1.2, how does the cost of this technology compare to that of in 1.3? Again, assume that the market is initially in the long run equilibrium that you found in 1.2, and it is required that every firm in this market to install this technology. Find out the new cost curve for a firm in this market. Find the short run output for each firm, market price, and profit. Then, find the long run output quantity per firm, market price and profit. Who would bear the cost of this technology? Something to think about; no answer is necessary. One defining feature of a com- petitive market is that firms behave competitively and are price takers. This seems to suggest that they have no control over the price. Consequently, it would suggest that, when firms face costly regulatory requirements, they have no choice but to bear these costs themselves (so that they would not be able to pass these costs to consumers). Is the above suggestion consistent with what you got in 1.3 and 1.4? What would be a 'better' intuition? (remember that you are in a graduate economics program and are learning how to think like economists!)
