Estimation and Analysis of Demand for Fast Food Meals

Checkers Pizza, is one of only two home delivery pizza firms serving the Muwaileh neighborhood of Sharjah. The manager and owner of Checkers Pizza, Ali Sultan knows that his customers are rather price-conscious. Pizza buyers in Muwaileh pay close attention to the price he charges for a home-delivered pizza and the price his competitor, Pizza Oven, charges for a similar home-delivered pizza.
Ali decides to estimate the empirical demand function for his firm’s pizza. He collects data on the last 24 months of pizza sales from his own company records. He knows the price he charged for his pizza during that time period, he also kept a record of the prices charged at Pizza Oven. Ali is able to obtain average household income figures from the Muwaileh Small Business Development Center. The only other competitor in the neighborhood is the local branch of McDonald’s. Ali is able to find the price of a Big Mac for the last 24 months from advertisements in old newspapers. He adjust his price and income data for the effects of inflation be deflating the Dirham figures, using a deflator he obtained from the Survey of Current Business.To measure the number of buyers in the market area (N), Ali collected data on the number of residents in Muwaileh. The data he collected are presented in the table below.

A supply function has also been estimated as follows:
Qs = -2603.56 + 384.94P

Data for Checkers Pizza
Observation Q P M P A1 PMac N
1 2,659 8.65 25,500 10.55 12.5 51000
2 2,870 8.65 25,600 10.45 13.5 51200
3 2,875 8.65 25,700 10.35 15.5 51800
4 2,849 8.65 25,970 10.3 10.5 51500
5 2,842 8.65 25,970 10.3 9.5 51600
6 2,816 8.65 25,750 10.25 9.5 52000
7 3,039 7.5 25,570 10.25 8.5 52000
8 3,059 7.5 25,950 10.15 11.5 51700
9 3,040 7.5 25,950 10 12.5 52100
10 3,090 7.5 26,120 10 17.5 52800
11 2,934 8.5 26,120 10.25 17.5 52100
12 2,942 8.5 26,120 10.25 18.5 51900
13 2,834 8.5 26,200 9.75 15 51800
14 2,517 9.99 26,350 9.75 11 51700
15 2,503 9.99 26,450 9.65 10.5 51100
16 2,502 9.99 26,350 9.6 12.5 51000
17 2,557 9.99 26,850 10 5.5 51250
18 2,586 10.25 27,350 10.25 5.5 51300
19 2,623 10.25 27,350 10.2 11.5 51400
20 2,633 10.25 27,950 10 11.5 51300
21 2,721 9.75 28,159 10.1 5.5 51500
22 2,729 9.75 28,264 10.1 5.5 51500
23 2,791 9.75 28,444 10.1 12 51100
24 2,821 9.75 28,500 10.25 12 51500

Section A:
Using the data shown above, estimate the parameters of the linear empirical demand function:
Qd = a + bP + cM + dPA1 + ePMac + fN
If any of the parameter estimates are not significant at the 5 percent level of significance, drop the associated explanatory variable from the model and estimate the demand function again.

  1. Perform a significance test of all the individual parameters at 5 percent level of significance. (Explain your procedure and show your calculation).
  2. Perform a significance test for the regression as a whole and explain and interpret the R-Square value.
  3. Write the estimated demand function and explain the nature of the good and its relationship with the other two goods.
  4. If the average income (M) = 12,000, Price of Pizza Oven = 10, and the price of Mac = 12
    i) Write the Direct demand function
    ii) The inverse demand function.
  5. Calculate the equilibrium price and quantity.
  6. Calculate the following elasticity’s and determine whether it is elastic, unitary elastic, or inelastic and explain why:
    i) Price elasticity of demand
    ii) Income elasticity of demand.
    iii) Cross-price elasticity of demand for Pizza Oven (PA1).
  7. At the equilibrium price and quantity, explain what will happen in the following cases:
    i) Increase in price by 10 percent.
    ii) Decrease in average income by 20 percent.
    iii) The price of Pizza Oven increase by 15 percent
  8. If Ali wishes to increase the quantity demanded by 25 percent what change in the price he should make?

Section B:
Using the given data in the table above, estimate the parameters for the log-linear empirical demand function:
Qd = aPbMcPA1dPMaceNf
If any of the parameter estimates are not significant at the 5 percent level of significance, drop the associated explanatory variable from the model and estimate the demand function again.

  1. Rewrite the function in its Ln format.
  2. Your estimated log-linear demand function for Checker Pizza is
    a. ___________________________.
  3. Does a log-linear specification work better than a linear specification of demand for Checker Pizza? Explain by comparing F-ratios, R2s, and t-ratios (or p-values).
  4. Using the estimated log-linear demand function, compute the price, income, and cross-price elasticity’s of demand. How do they compare to the estimated elasticity’s for the linear demand specification?
  5. If the price of Checker pizza (P) = 9, average income (M) = 12,000, Price of Pizza Oven = 10, and the price of Mac = 12, using the estimated log-linear function, compute the quantity demanded.