The Maxwell School

Syracuse University

Syracuse University

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:

- 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.
- 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.
- Make sure the TC cells are filled in with the data for the first case.
- Click on one of the cells in the Computations section and use Insert > Table to turn it into a data table.
- Add appropriate formulas to compute P, TR, TC, and Profit.
- Add a formula for AC. The first row will have an error since Q=0: delete that entry and leave the cell blank.
- 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. - 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.
- Add a formula to the Gains column equal to the gains from trade on that unit: P-MC.
- 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.
- Construct a figure showing P, AC, MR and MC to help identify the key Qs.
- 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.
- Repeat for the other two cases.

Save and submit the results!

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URL: https://wilcoxen.maxwell.insightworks.com/pages/9111.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 04/02/2024

URL: https://wilcoxen.maxwell.insightworks.com/pages/9111.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 04/02/2024