Question

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.

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

A. Using the data in Table 1, specify a linear functional form for the demand for home delivery pizza, and run a regression to estimate the demand for pizza.

B. Using Excel Data Analysis, estimate the parameters of the empirical demand function specified in part a. Write your estimated demand equation.

C. Evaluate your regression results by examining signs of parameters, p-values (or t-ratios), and the R².

Answer 1

A. Let's term the different variables as follows:

Demand (Q) - dependent variable

Independent variables

Pizza Price (P) expected to have a negative sign

Household Income (M) expected to have a positive sign

Price of Pizza at Al's (A) expected to have a positive sign, as it is a competitive product

Price of Big Mac (B) expected to have a positive sign, as it is a competitive product

Constant (C)

The demand function will be:

Q = C + xP + yM + zA + wB

B. Using Linest function in Excel we obtain the following estimated demand equation

Q = 1183.80 - 213.42P + 0.091M + 101.30A + 71.84B

The signs are as expected in part A.

Just for record, below is the output of the Linest function

71.8447991	101.3029	0.091088	-213.4219	1183.802
27.0997018	38.74776	0.01241	13.486317	506.298
0.95546183	42.41123	#N/A	#N/A	#N/A
101.900098	19	#N/A	#N/A	#N/A
733155.802	34175.53	#N/A	#N/A	#N/A

C. R2 in our estimated equation is 0.955, which is very high (explains almost 95.5% of the change in Q with the equation we estimated)

t-values are calculated by diving the values in the first row with the second row and are as follows, and all of these are significant:

t-values
2.65112877	2.614418	7.339957	-15.82507	2.338154
B	A	M	P	C