# D30: Choosing the Level of Output

A producer has a total cost curve given by TC(Q)=4000+20*Q^2 and is the only provider of its product in a market with a demand curve given by WTP(Q) = 1500-10*Q. Please use the template in Teams to build a spreadsheet to analyze the producer's optimal output for two cases: (1) the producer is a public organization interested in maximizing the number of clients it serves (Q max), and (2) the producer is a private firm interested in maximizing its profits (\Pi max).

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.
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. For this particular producer, the coefficients should be 4000, 0 and 20.
3. Insert a table in the output options area.
4. Add an appropriate formula to the P column to compute the price for the row's Q using the WTP equation.
5. Add an appropriate formulas to compute TR, TC, and profit.
6. Add formulas for AR and AC. The first row will have errors since Q=0; delete those entries and leave the cells blank.
7. Add a formula for the difference between AR and AC. That will make it easy to find the output maximizing Q.
8. 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 MR will be TR(1)-TR(0). The first row will have errors since there's no previous row; delete those entries and leave the cells blank.
9. Add a column for the difference between MR and MC. That will make it easy to find the profit maximizing Q.
10. Construct three separate figures: (1) a plot showing TR, TC and Profit; (2) a plot showing AR and AC; and (3) a plot showing MR and MC.
11. Finally, find the output-maximizing and profit-maximizing levels of output and answer the questions at the bottom.

Save and submit the results!

URL: https://wilcoxen.maxwell.insightworks.com/pages/9098.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/02/2024