Q P Dom M Income P Hut AVC 1 2,750 $8.65 $25,500.00 $10.55 4.125 2 2,800 $8.65 $25,600.00 $10.45 4.64 3 2,875 $8.65 $25,700.00 $10.35 5.469 4 2,849 $8.65 $25,970.00 $10.30 5.174 5 2,842 $8.65 $25,970.00 $10.30 5.096 6 2,816 $8.65 $25,750.00 $10.25 4.811 7 3,039 $7.50 $25,750.00 $10.25 7.516 8 3,059 $7.50 $25,950.00 $10.15 7.788 9 3,100 $7.50 $25,950.00 $10.00 8.36 10 3,090 $7.50 $26,120.00 $10.00 8.219 11 2,934 $8.50 $26,120.00 $10.25 6.168 12 2,942 $8.50 $26,120.00 $10.25 6.266 13 2,834 $8.50 $26,200.00 $9.75 5.007 14 2,517 $9.99 $26,350.00 $9.75 2.121 15 2,503 $9.99 $26,450.00 $9.65 2.021 16 2,502 $9.99 $26,350.00 $9.60 2.014 17 2,557 $9.99 $26,850.00 $10.00 2.418 18 2,500 $10.25 $27,350.00 $10.25 2 19 2,623 $10.25 $27,350.00 $10.20 2.952 20 2,633 $10.25 $27,950.00 $10.00 3.037 21 2,700 $9.75 $28,159.00 $10.10 3.64 22 2,729 $9.75 $28,264.00 $10.20 3.918 23 2,790 $9.75 $28,444.00 $10.25 4.535 24 2,800 $9.75 $28,500.00 $10.50 4.64 AVC =21.998728 -0.022999Q + 0.000006 Q2 TVC = AVC*Q = 21.998728Q -0.022999Q2 +0.000006 Q3 MC = TVC' = dTVC/dQ = d(21.998728Q -0.022999Q2 +0.000006 Q3) / dQ MC = 21.998728 - (2) 0.022999Q + (3) 0.000006 Q2 MC = 21.998728 - 0.045998 Q + 0.000018 Q2 MR = 22.159836 - 0.008632 Q, from (e) MC = 21.998728 - 0.045998 Q + 0.000018 Q2, from (j) set MR = MC 22.159836 - 0.008632 Q = 21.998728 - 0.045998 Q + 0.000018 Q2 , or 22.159836 - 0.008632 Q - (21.998728 - 0.045998 Q + 0.000018 Q2) = 0 0.161108 + 0.037366 Q - 0.000018 Q2 = 0 To solve by quadratic problem solver, need to reverse the order - 0.000018 Q2 + 0.037366 Q + 0.161108 = 0 From (d), P dom = 22.159836 - 0.004315866 Q, so P* = 22.159836 - 0.004315866* 2080.191591 P* = 22.159836 - 8.977828 P* = $13.18201 P* = $13.18 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), 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. Below are a series of questions that lead you to find optimal output and prices for Dom's Pizza (profit-maximizing). Note: carry regression output (coefficients) decimals to 6 places in the equations. (Format your data to 6 decimal places and do the multiplication in 6 decimal places.) (a) Using your data table, run a regression that would enable you to estimate the weekly demand for Dom's pepperoni pizza as a function of its price, consumer income, and Pizza Hut's price. Show regression output. Which coefficient is significant? Why? (b) write the estimated weekly demand equation for Domino's pepperoni pizza. (c) Suppose for a week in the future it is expected that M=$30,000 and PHUT = $10. Write the demand function for Domino's pepperoni pizza that you'd use for that week. (d) Using your estimated demand function, write the inverse demand equation (solve for P). (e) From the inverse demand function, write the estimated equation for marginal revenue (MR). (f) Now let's move into the cost equation. From your data in part (a) new data table that allows us to estimate Domino's AVC (average variable cost) regression equation (AVC = a + bQ +c Q2). Note: for multivariate regressions in Excel, the multiple explanatory variables MUST be adjacent one another for the input range of X to work properly. (g) Using the data table, run a regression that will enable you to estimate the company's AVC. Show the regression output. Which coefficient is significant? Why? (h) Write Domino's estimated AVC equation. (i) From your AVC equation, write Domino's estimated TVC (total variable cost) equation, where TVC = AVC*Q. (j) Write Domino's estimated MC equation. (k) Using your estimated equations for MR (part e) and MC (part j), what is Domino's optimal number of pepperoni pizzas to sell per week that results in maximum profits for Domino's? (find Q* by setting MR = MC). (l) If Domino's wants to maximize its profit, what price should it set for its pepperoni pizzas for an average store?