Question 1. You're a financial analyst for Domino's Pizza. Your department has collected weekly data for an "average" Domino's store in the USA over the past 24 weeks. Since Domino's considers Pizza Hut as its main competitor, your department also keeps weekly information on Pizza Hut.
You were given weekly data for Domino's Pepperoni Pizza sales (starting with the oldest data first), and both Domino's and Pizza Hut's prices for their pepperoni pizzas, along with the average income of people who normally buy pepperoni pizza, and the average variable cost of Domino's pepperoni pizza. (You can copy these data below and paste it in an excel spread sheet.)
| Weeks |
Q |
P (Domino's) |
M |
P (Pizza Hut) |
AVC |
| 1 |
2,750 |
$8.65 |
$25,500.00 |
$10.55 |
4.13 |
| 2 |
2,800 |
$8.65 |
$25,600.00 |
$10.45 |
4.64 |
| 3 |
2,875 |
$8.65 |
$25,700.00 |
$10.35 |
5.47 |
| 4 |
2,849 |
$8.65 |
$25,970.00 |
$10.30 |
5.17 |
| 5 |
2,842 |
$8.65 |
$25,970.00 |
$10.30 |
5.1 |
| 6 |
2,816 |
$8.65 |
$25,750.00 |
$10.25 |
4.81 |
| 7 |
3,039 |
$7.50 |
$25,750.00 |
$10.25 |
7.52 |
| 8 |
3,059 |
$7.50 |
$25,950.00 |
$10.15 |
7.79 |
| 9 |
3,100 |
$7.50 |
$25,950.00 |
$10.00 |
8.36 |
| 10 |
3,090 |
$7.50 |
$26,120.00 |
$10.00 |
8.22 |
| 11 |
2,934 |
$8.50 |
$26,120.00 |
$10.25 |
6.17 |
| 12 |
2,942 |
$8.50 |
$26,120.00 |
$10.25 |
6.27 |
| 13 |
2,834 |
$8.50 |
$26,200.00 |
$9.75 |
5.01 |
| 14 |
2,517 |
$9.99 |
$26,350.00 |
$9.75 |
2.12 |
| 15 |
2,503 |
$9.99 |
$26,450.00 |
$9.65 |
2.02 |
| 16 |
2,502 |
$9.99 |
$26,350.00 |
$9.60 |
2.01 |
| 17 |
2,557 |
$9.99 |
$26,850.00 |
$10.00 |
2.42 |
| 18 |
2,500 |
$10.25 |
$27,350.00 |
$10.25 |
2 |
| 19 |
2,623 |
$10.25 |
$27,350.00 |
$10.20 |
2.95 |
| 20 |
2,633 |
$10.25 |
$27,950.00 |
$10.00 |
3.04 |
| 21 |
2,700 |
$9.75 |
$28,159.00 |
$10.10 |
3.64 |
| 22 |
2,729 |
$9.75 |
$28,264.00 |
$10.20 |
3.92 |
| 23 |
2,790 |
$9.75 |
$28,444.00 |
$10.25 |
4.54 |
| 24 |
2,800 |
$9.75 |
$28,500.00 |
$10.50 |
4.64 |
Below are a series of questions that lead you into finding optimal output and prices for Dom's pizza (profit maximizing). Here are some resources:
1. (AVC and MC). For an example of estimating AVC and SMC, look at lecture 12, slides #31-#34 and #41, #43.
2. (MR). Recall how to estimate the direct demand equation (and the inverse price line) from Checker Pizza from previous lecture 9. Also lecture 12, slides #40 and #42.
3. (MR = MC). To max profit, set ____ to _____. Often to find the solution we need to use an online quadratic problem solver, (Math is Fun!) Look at lecture 12, slides #36, #37, and #44. (Once you have solved for Q, substitute it into the price line (inverse demand equation) and solve for Dom's price.
Here we go!
a. Using the prior 24 weeks of data, create a spreadsheet (with data) and run a regression that would enable you to estimate weekly demand (direct demand equation) for Domino's pepperoni pizza.(Attach excel spreadsheet showing data used and regression output.)(10 pts.)
b. Write your estimated weekly demand equation for Domino's peperoni pizza.
c. Suppose for the next 4 weeks it is assumed that M=$30,000 and PHUT = $10. Write the direct demand equation for Domino's pepperoni pizza that you'd use for those weeks.
d. Using the direct demand equation, write the inverse demand equation (solve for P).
e. Write the estimated equation for marginal revenue.
f. Look at the AVC and Q data that was given on page 1, and create a new data table that allows you to run a separate regression that forecastsDomino's AVC equation (AVC = a + bQ +c Q^2). On this AVC spreadsheet show the data that was used to estimate AVC, and the regression output.)
g. Write Domino's estimated AVC equation.
h. Write Domino's estimated TVC equation.
i. Write Domino's estimated MC equation.
j. Using your estimated equations for MR (part e) and MC (part i), what is Domino's optimal output of pizza per week?
k. If Domino's is a profit maximizer, what PRICE should it set for their pepperoni pizzas for an average store? (You might want to use Math is Fun's Quadratic Problem Solver?)