# Managrial Economics Project Essay

Team 20| MANAGIRAL ECONOMICS PROJECT 1| Estimation of the Demand for Combo 1 meals| | Corey Siragusa 106549438| Yujing Zhang 108672624 | Gary Zhao 108693441| 11/7/2012| a) Using the data in Table 1, specify a linear functional form for the demand for Combination 1 meals, and run a regression to estimate the demand for Combo 1 meals. According to the passage, we know that the Quantity of meals sold by Combination (Q) is related to the average price charged (P) and the dollar amount spent on newspaper ads for each week in 1998(A).

The price will influence the quantity of demand with inverse relation, and ads may lead to change of demand with positive relation. Household income and population in the suburb did not change enough to warrant inclusion in the demand analysis, so we don’t think these variables should be involved in the function. What’s more, prices charged by other competing restaurants during 1998 could not be provided, so we have to regard it as parts of error item. In summary, we specify a linear functional form for the demand as: Qd=f(P,A)=? + ? P + ? A + ? And we will run a regression to estimate the demand with:

Qd =f(P,A)=^? + ^? P + ^? A. b) Using statistical software, estimate the parameters of the empirical demand function specified in part a. Write your estimated demand equation for Combination 1 meals. Using Excel2010, we get the parameters of the empirical demand function specified in Part a. The Summary Output Table is attached as appendix. From that table, we get: ^? =100626. 05, ^? =-16392. 65, ^? =1. 58. So we estimate the demand equation as blow: Qd= 100626. 05-16392. 65P +1. 58A c) Evaluate your regression results by examining signs of parameters, p-values (or t-ratios), and the adjusted R2.

According the Summary Output Table, we get that: p-values are all much smaller than 5%, and t-ratios are all larger than 2. This means that there is less than 5 in 100 chance that the true coefficient of price is actually 0. So we can be 95% confident that the real, underlying value of the coefficient that you are estimating falls somewhere in that 95% confidence interval. We can have strong confident to conclude that P and A variable has some correlation with Q. However, the Adjusted R-square equals to 0. 2337, which is not every large. That is to say, P and A are able to explain only 23. 37% changes of quantity of demand. ) Discuss how the estimation of demand might be improved. From Part C, we find that the adjusted R-square is not very high. So we should increase the adjusted R-square by increasing number of variables. We believe that the estimation of demand might be improved, if we can collect more information about competitors, including their price, advertising, product improvement, etc. And the population of tourists can be consideration, even though the permanent population didn’t change obviously. e) Using your estimated demand equation, calculate an own-price elasticity and an advertising elasticity.

Compute the elasticity values at the sample mean values of the data in Table 1. Discuss, in quantitative terms, the meaning of each elasticity. When Mean of P=4, Mean of A=10009, then Qd= 100626. 05-16392. 65P +1. 58A=50869. 67 Own-price elasticity =-16392. 65*4/50869. 67= -1. 289 Advertising elasticity=1. 58*10009/50869. 67=0. 3109 The own-price elasticity is -1. 289, which means that if the price goes up \$1, the quantity will go down 1. 289, and the revenue will drop. The advertising elasticity is 0. 3109, which means that if the investment on ads increases \$1, the quantity will go up 0. 109. f) If the owner plans to charge a price of \$4. 15 for a Combination 1 meal and spend \$18,000 per week on advertising, how many Combinations 1 meals do you predict will be sold each week? Qd= 100626. 05-16392. 65(\$4. 15) +1. 58(\$18,000) = 61,036. 55 61037 Combinations 1 meals are predicted to be sold each week in this situation. h) If the owner spends \$18,000 per week on advertising, write the equation for the inverse demand function. Then, calculate the demand price for 50,000 Combination 1 meals. Qd= 100626. 05-16392. 65P +1. 58(\$18,000) = 129,066. 5 -16,392. 65P P = F(Q) = 7. 8734 – (Q / 16392. 65) P = 7. 8734 – (50,000 / 16392. 65) = \$4. 82 The demand price for 50,000 Combination 1 meals is \$4. 82. Appendix SUMMARY OUTPUT| | | | | | | | | | | | Regression Statistics| | | | | Multiple R| 0. 513597898| | | | | R Square| 0. 263782801| | | | | Adjusted R Square| 0. 233733119| | | | | Standard Error| 19176. 2901| | | | | Observations| 52| | | | | | | | | | | ANOVA| | | | | | | df| SS| MS| F| Significance F| Regression| 2| 6456033545| 3228016773| 8. 77822282| 0. 000551628| Residual| 49| 18018774997| 367730102| | |

Total| 51| 24474808542|  |  | | | | | | | | | Coefficients| Standard Error| t Stat| P-value| | Intercept| 100626. 0497| 19216. 40273| 5. 23646653| 3. 42163E-06| | X Variable 1| -16392. 6523| 5105. 3048| -3. 210905703| 0. 002337804| | X Variable 2| 1. 576333781| 0. 603179309| 2. 613375091| 0. 011873731| | | Lower 95%| Upper 95%| Lower 95. 0%| Upper 95. 0%| | Intercept| 62009. 24265| 139242. 8568| 62009. 24265| 139242. 8568| | X Variable 1| -26652. 1464| -6133. 158194| -26652. 1464| -6133. 15819| | X Variable 2| 0. 364199578| 2. 788467984| 0. 364199578| 2. 788467984|  |