Intermediate Microeconomics
Excel Project 3: Cournot Oligopoly and Competition
DUE 12/4/20 via Canvas
Part 1. Load Cournot_competition.xls into Excel. The first spreadsheet is titled “2 firm Cournot.” Consider two firms, Carpenter and Hanover, competing in Cournot fashion.
1. Using the parameters given, code into cells C8 through C37, Carpenter’s reaction function values to its output conjecture (in cells B8 through B37). Do the same for Hanover in cells D8 through D37. (These values will be the same)
2. Now, calculate Hanover’s “inverse reaction function” (this is only done to facilitate graphing). This is done as follows: “=70-10-2*B#”. Fill these values in E8 through E37.
3. Highlight columns B, C and E (7 through 37), and use Excel to create a “scatter plot” of these reaction functions.
4. What does this graph indicate as the Nash Equili
ium output levels for Hanover and Carpenter?
5. Using this information, calculate market price, Carpenter’s profit, and Hanover’s profit.
6. For the Collusion, case (the table begins in B40), fill in the Marginal Revenue values, the Marginal Cost values (which equals 10 in every cell because MC is a constant value). Then find, the equili
ium output level (this will be only one value), and use this to calculate market price and each firm’s profits (assume each firm receives 50% of total profits). Compare with 5 and explain.
7. Notice in cell P4 we have dropped Hanover’s MC to $4. In columns P and Q calculate its new reaction function and inverse reaction function.
8. On a new graph, create a scatter plot identical to the one you created in 3, but add to it the reaction function information in column Q.
9. Find the new equili
ium output levels, and use those to calculate market price, an each firms’ profits.
10. Compare the market shares between 9 and 5. Do these results make sense? Explain.
11. Compare market price between 9 and 5. Recall the Hanover’s MC fell by $6, by how much did market price change? What does this suggest about price movements in Cournot Oligopolies? How does this compare with the empirical record as discussed in class?
Part 2. Consider an industry comprised of N number of identical Cournot-competing firms. Market demand is given by P=a-bQ, where P is price and Q is total industry output. Note, Q = q1 +q2+q3+…, which then results in Q = Nq (since all N firms are identical, q1=q2=q3-…). Therefore, we can write P = a-bNq.
For a given firm i, we can write demand as follows: P = a-b(N-1)qj – bqi, where, qj simply refers to any other firm except firm i. It can be shown that firm i’s marginal revenue can be written as follows: MR = P = a-b(N-1)qj – 2bqi.
1. Set MR = MC and find firm i’s Best Response Function (RF).
2. Since each firm produces the same level of output, set qi = qj in your (RF) and find the expression for the equili
ium level of firm output.
For parts 3, 4, and 5, please do all tasks in Excel file Cournot_Competition.xls. Use the “N firm case” spreadsheet.
4. Notice, that in this example, a=100, b = 2, and c = 5, and that N runs from 1 to 50 in column A. Use your result from 2 to populate columns B. Then calculate values for C through G using standard formulations. Create charts for each of the above in the same Excel Spreadsheet.
5. In separate paragraphs (3-to-5 sentences) describe the patterns for firm output, industry output, market price, firm profit, industry profit, and the Lerner index. Make certain you explain the economic behavior being illustrated as the number of firms in an industry increases. Please write these in Sheet2 of your Excel file (wrap text).
6. Focus just on the market price column. To what value does market price appear to be approaching as N increases? What does this result suggest about the relationship between Cournot competition and Perfect Competition?
When completed, upload both this WORD file (with your name in the file title), and your EXCEL file (with your name in the file name)