# D32: Checking the Efficiency of a Monopoly

A monopoly producer has a demand curve given by WTP(Q) = 1500-10*Q. The producer's cost curve is given by TC=A+B*Q+C*Q^2 and the analysis will consider three cases with different values of A, B and C. Please use the template in Teams to build a spreadsheet to determine three values of Q for each cost function case: (1) the profit-maximizing Q; (2) the output maximizing Q; and (3) the efficient Q.

Here are the specific steps to carry out to do the analysis:

1. The spreadsheet has cells labeled WTP_A and WTP_B. They can hold the coefficients for a WTP equation that looks like this: WTP(Q) = A + B*Q. For this producer, the coefficients should be 1500 and -10 and are already filled in.
2. It also has cells labeled TC_A, TC_B and TC_C. They can hold the coefficients in a TC equation that looks like this: TC(Q) = A + B*Q + C*Q^2. The coefficients for the three cases are shown in columns to the right.
3. Make sure the TC cells are filled in with the data for the first case.
4. Click on one of the cells in the Computations section and use Insert > Table to turn it into a data table.
5. Add appropriate formulas to compute P, TR, TC, and Profit.
6. Add a formula for AC. The first row will have an error since Q=0: delete that entry and leave the cell blank.
7. Add formulas for MR and MC that compute the difference between the current row's TR or TC and the TR or TC on the previous row. For example, in row 1 MC will be TC(1)-TC(0). Start in the row for Q = 1 and erase the Q = 0 values after Excel fills in the column.
8. Add formulas to the P-AC and MR-MC columns starting in the row for Q = 1 (erase the values in Q = 0). These will make it easy to find the output and profit maximizing Qs.
9. Add a formula to the Gains column equal to the gains from trade on that unit: P-MC.
10. Add a formula to the Tot SS column to compute the cumulative sum of the Gains column. The value for Q=0 is already entered as 0. The formula for the Q=1 row should be the previous entry in the Tot SS column plus the Gains entry on the Q=1 row. Note that Excel won't autofill the whole column because of the manually-entered 0 for Q=0 so you'll need to copy and paste the formula for the remaining rows.
11. Construct a figure showing P, AC, MR and MC to help identify the key Qs.
12. Answer the questions in the Analysis section at the top. The DWL cell should be the difference between the efficient SS and the SS achieved in the case being analyzed.
13. Repeat for the other two cases.

Save and submit the results!

URL: https://wilcoxen.maxwell.insightworks.com/pages/9111.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/02/2024