Assume that Q = quantity of pi

1. Assume that Q = quantity of pizza (in cents), X1 = price of pizza, X2 = tuition (in thousands of dollars), X3 = price of soft drinks (in cents), and X4 = location (1 for urban setting):

Q X1 X2 X3 X4

10 100 14 120 1
12 100 16 95 1
13 90 8 110 1
14 95 7 90 1
9 110 11 100 0
8 125 5 100 0
4 125 12 125 1
3 150 10 150 0
15 80 18 100 1
12 80 12 90 1
13 90 6 80 0
15 100 5 75 0
12 110 13 100 1
10 110 10 125 0
10 125 14 130 0
12 110 15 80 1
11 150 16 90 0
12 100 12 95 1
10 150 12 100 0
8 160 10 90 0
9 150 13 95 0
10 135 15 100 1
11 125 16 95 1
12 100 17 100 0
13 75 10 100 1
10 100 12 110 1
9 110 6 125 0
8 125 10 90 0
8 150 5 80 1
5 150 10 95 0

a. Estimate the linear demand function with Q as the dependent variable and X1 as the independent variable. Comment fully on the results and discuss the identification problem.
b. Estimate the linear demand function with Q as the dependent variable and X1, X2, X3, and X4 as the independent variables. Comment fully on the results. Calculate the elasticity of demand when X1 = 100, X2 = 10, X3 = 90, and X4 = 1. At what value of X1 do we have unitary elasticity (assume X2 = 10, X3 = 90, and X4 = 1)?
c. Take the natural logarithm of Q, X1, X2, and X3 (not X4) and estimate the exponential demand function (or Cobb-Douglas function). Comment fully on the results. What is the value of the price elasticity of demand? What is the value of the cross-price elasticity of demand?