Assume that Q = quantity of pizza, X1 = price of pizza (in cents), X2 = tuition (in thousands of dollars), X3 = price of soft drinks (in cents):
Q X1 X2 X3
Pizza Price of Pizza Tuition Price of Soda
12 110 13 100
10 110 10 125
10 125 14 130
12 110 15 80
11 150 16 90
12 100 12 95
10 150 12 100
8 160 10 90
9 150 13 95
10 135 15 100
11 125 16 95
12 100 17 100
13 75 10 100
10 100 12 110
9 110 6 125
8 125 10 90
8 150 5 80
4 100 0 95
a) Estimate the linear demand function with Q as the dependent variable and X1 as the independent variable. Is this a good model? How do you know (explain relevant results)? The form of the model is .
b) Estimate the linear demand function with Q as the dependent variable and X1, X2, X3, as the independent variables. Is this a better model than in a)? How do you know (explain relevant results)?
c) Take the natural logs of Q, X1, X2, and X3 and estimate this version of the D function. Is this a better model than that of a) or b)? Why (explain relevant results)?
d) What is the value of the price elasticity of demand? What is the value of the cross-price elasticity of demand?
Input the following data into Excel.
10) Assume we have the following time series data on variable Y below:
YEAR Y
1991 8649
1992 8660
1993 8680
1994 8726
1995 8740
1996 8760
1997 8783
1998 8805
1999 8812
2000 8854
2001 8841
2002 8869
2003 8893
2004 8883
2005 8888
2006 8904
2007 8913
2008 8913
2009 8923
2010 8948
2011 8962
a) Fit a simple trend model to the time series data and discuss the findings.
This model can be written as
b) Fit a quadratic trend model to the time series and discuss the findings.
Hint: [If the model in a) is written as, how is the model in b) different?]
c) Compare your results in part b) to part a)
d) Use the best of the two models to forecast the 2012 value of Y.