4.10 Consider a market for electrical energy that is supplied by two generating com- panies whose cost functions are CA = 36 - PA $/h CB = 31 - PB S/h The inverse demand curve for this market is estimated to be л=120-DS/MWh Assuming a Cournot model of competition, use a table similar to the one used in Example 4.8 to calculate the equilibrium point of this market (price, quantity, production and profit of each firm). (Hint: Use a spreadsheet. A resolution of 5 MW is acceptable) 104 4.11 4 PARTICIPATING IN MARKETS FOR ELECTRICAL ENERGY Write and solve the optimality conditions for Problem 4.10. 4.10 PA = 25 MW; PB = 30 MW; D = 55 MW; л = 65 $/MWh; NA = $725; B = $1,020 4.11 PA = 26.33 MW; PB = 31.33 MW; D = 55 MW; л = 57.66 $/MWh; 2A = $694; B = $982

May and Raj me the only two growers who provide organically grown corn to a local grocery store. They know that if they cooperated and produced less corn, they could raise the price of the com. If they work independently, they will each earn 100. If they decide to work together and both lower their output, they call each earn 150. If one person lowers output and the other does not, the person who lowers output will earn $1 and the other person will capture the entire market and will earn 200. Table 10.6 represents the choices available to Mary and Raj. What is the best choice for Raj if he is sole that Mary will cooperate? If Mary thinks Raj will cheat, what should Mary do and why? What is the prisoners dilemma result? What is the preferred choice if they could ensure cooperation? A = Work independently; B = Cooperate and Lower Output. (Each results entry lists Rajs earnings first, and Marys earnings second.)

A firm in a perfectly competitive industry has patented a newprocess for making widgets. The new process lowers the firm’saverage cost, meaning that this firm alone (although still aprice taker) can earn real economic profits in the long run. a. If the market price is $20 per widget and the firm’s marginalcost is given by MC=0.4q , where q is the dailywidget production for the firm, how many widgets willthe firm produce? b. Suppose a government study has found that the firm’snew process is polluting the air and estimates the socialmarginal cost of widget production by this firm to be. If the market price is still $20, what is thesocially optimal level of production for the firm? Whatshould be the rate of a government-imposed excise tax tobring about this optimal level of production? c. Graph your results.

Ajax Cleaning Products is a medium-sized firm operating in an industry dominated by one large firm—Tile King. Ajax produces a multiheaded tunnel wall scrubber that is similar to a model produced by Tile King. Ajax decides to charge the same price as Tile King to avoid the possibility of a price war. The pnce charged by Tile King is $20,000. Ajax has the following short-run cost curve: TC=800,0005,000Q+100Q2 Compute the marginal cost curve for Ajax. Given Ajaxs pricing strategy, what is the marginal venue function for Ajax? Compute the profit-maximizing level of output for Ajax. Compute Ajaxs total dollar profits.