Question

Estimating Demand for Pizza Firm

Below is a case on estimation and analysis of demand for home delivery pizza.

Read the case carefully and use the appropriate techniques given in the text book on demand estimation and analysis and make your decisions, judgments and evaluation based on the results.

Consider Al Barkat Pizza, one of the home delivery pizza firms serving the Muweileh, Sharjah. The manager and owner of Barkat Pizza, Mariam, knows that her customers are rather price-conscious. She knows that Pizza buyers in Muwilah pay close attention to the price she charges for a home-delivered pizza and the price her competitors charge.

Mariam decides to estimate the empirical demand function for her firm’s pizza. She collects data on the last 24 months of pizza sales from her own company records. She knows the price she charged for her pizza during that time period, and she also has kept a record of the prices charged at Al’s Pizza Oven. She is able to obtain average household income figures from the Small Business Development Center. The only other competitor in the neighborhood is the local branch of McDonald’s. Mariam is able to find the price of a Big Mac for the last 24 months from advertisements in old newspapers. The data she collected are presented in table 1. (12 Marks)

Table 1: Data for Checkers Pizza

Observation	Quantity of Pizza (Q)	Pizza Price (P)	Household Income (M)	Price of Pizza at AIs (	Price of Big Mac (
1	2659	8.65	25500	10.55	1.25
2	2870	8.65	25600	10.45	1.35
3	2875	8.65	25700	10.35	1.55
4	2849	8.65	25970	10.30	1.05
5	2842	8.65	25970	10.30	0.95
6	2816	8.65	25750	10.25	0.95
7	3039	7.50	25750	10.25	0.85
8	3059	7.50	25950	10.15	1.15
9	3040	7.50	25950	10.00	1.25
10	3090	7.50	26120	10.00	1.75
11	2934	8.50	26120	10.25	1.75
12	2942	8.50	26120	10.25	1.85
13	2834	8.50	26200	9.75	1.50
14	2517	9.99	26350	9.75	1.10
15	2503	9.99	26450	9.65	1.05
16	2502	9.99	26350	9.60	1.25
17	2557	9.99	26850	10.00	0.55
18	2586	10.25	27350	10.25	0.55
19	2623	10.25	27350	10.20	1.15
20	2633	10.25	27950	10.00	1.15
21	2721	9.75	28159	10.10	0.55
22	2729	9.75	28264	10.10	0.55
23	2791	9.75	28444	10.10	1.20
24	2821	9.75	28500	10.25	1.20

The question is on the picture please i need it ASAP

d. If the owner fixed to charge a price of pizza P = 9.05. For the given values of M = 26,614, Pa = 10.12, and PBMac = 1.15 Calculate estimated the demand elasticities of P, M, , Pa, and, PBMac

Answer 1

Using the above data, a linear regression can be performed for the following equation Q = Bo + B1P + B2M + B3PAI + B4PBMac + U The following results is obtained using Microsoft Excel. Please note that I have considered the numbers with 2 decimal places, but for calculations, the exact number has been used.

0.98 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA MS Significance F F 101.90 Regression Residual Total 0.00 183288.95 1798.71 733155.80 34175.53 767331.33 19 t Intercept Pizza Price (P) Household Income (M) Price of Pizza at Als Price of Big Mac Coefficients 1183.80 -213.42 0.09 101.30 71.84 Standard Error 506.30 13.49 0.01 38.75 27.10 Stat 2.34 -15.83 7.34 2.61 2.65 P-value 0.03 0.00 0.00 0.02 0.02 Lower 95% 124.11 -241.65 0.07 20.20 15.12 Upper 95% 2243.50 -185.19 0.12 182.40 128.57 Lower 95.0% 124.11 -241.65 0.07 20.20 15.12 Upper 95.0% 2243.50 -185.19 0.12 182.40 128.57

Using the above data, a linear regression can be performed for the following equation Q = Bo + B1P + B2M + B3 Pai + B4PBMac + U The following results is obtained using Microsoft Excel. Please note that I have considered the numbers with 2 decimal places, but for calculations, the exact number has been used. Using the regression coefficients At P = 9.05, M = 16614, PAI = 10.12 and PBMac = 1.15, the estimated demand would be 1183.80 + (-213.42)9.05 + (0.09)16614 + (101.30)10.12 + (71.84)1.15 = 2784.36 Demand elasticity of P = ? 429.05 42) 2784.36 = -0.69 Demand elasticity of M = m = (0.09) 246.46 = 0.87 Demand elasticity of Par = 2 PAL = (101.30)278436 = 0.37 Demand elasticity of PsMac = cap Penge = (71.84) 27456 = 0.03

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You may also get the elasticity estimates directly by estimating the logarithmic version of the model, where the coefficients are directly interpreted as elasticity estimates. I have not used the below result since the intercept is statistically not significant. If you use this model, to predict sales at the given price, income and prices of related goods, you need to take the exponential after calculating the estimated ln(Q). The regression result of the logarithmic form is as follows, where all the variables are transformed with natural logarithms.

Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.97 0.95 0.94 0.02 ANOVA df S S 88.72 MSF 0.02 0.00 Significance F 0 .00 Regression Residual Total 0.09 .01 0.10 190 23 Intercept In(PP) In(M) In(PAI) In(PBM) Coefficients Standard Errort Stat P-valueLower 95% Upper 95% Lower 95.0% -0.73 1.31 -0.55 0.59 -3.48 2.03 -3.48 -0.66 0.04 -14.800.00 -0.76 -0.57 -0.76 0.88 0.13 6.78 0.00 0.61 1.15 0.61 0.51 0.15 3.40 0.00 0.19 0.19 0.03 0.01 2.65 0.02 0.01 0.05 0.01 Upper 95.0% 2.03 -0.57 1.15 0.82 0.05 0.82