In a study published in 1980, B. B. Gibson estimated the following price and income elasticities of demand for six types of public goods:
STATE ACTIVITY PRICE INCOME
ELASTICITY ELASTICITY
Aid to needy people -0.83 0.26
Pollution Control -0.99 0.77
Colleges and universities -0.87 0.92
Elementary school aid -1.16 1.14
Parks and recreation areas -1.02 1.06
Highway construction and -1.09 0.99
maintenance
Do these public goods conform to the law of demand

Problem 15 (b):
Integrating Problem Starting with the data:
YEAR Y X1 X1
1986 72 $10 $2,000
1987 81 9 2,100
1988 90 10 2,210
1989 99 9 2,305
1990 108 8 2,407
1991 126 7 2,500
1992 117 7 2,610
1993 117 9 2,698
1994 135 6 2,801
1995 135 6 2,921
1996 144 6 3,000
1997 180 4 3,099
1998 162 5 3,201
1999 171 4 3,308
2000 153 5 3,397
2001 180 4 3,501
2002 171 5 3,689
2003 180 4 3,800
2004 198 4 3,896
2005 189 4 3,989
And the data on the price of a related commodity for the years 1986 to 2005 given below, we estimated the regression for the quantity demanded of a commodity (which we now label Qx, on the price of the commodity (which we now label Px), consumer income (which we now label Y), and the price of the related commodity (Pz), and we obtained the following results. ( If you can, run this regression yourself; you should gt results identical or very similar to those given below.)
YEAR 1986 1987 1988 1989 1990
Pz ($) 14 15 15 16 17
YEAR 1991 1992 1993 1994 1995
Pz ($) 18 17 18 19 20
YEAR 1996 1997 1998 1994 2000
Pz 20 19 21 21 22
YEAR 1996 1997 1998 1994 2000
Pz 23 23 24 25 25
Qx = 121.86 - 9.50Px + 0.04Y - 2.21Pz
(-5.12) (2.18) (-0.68)
R2 = 0.9633 F = 167.33 D-W = 2.38
(a) Evaluate the above regression results.
Note: (b) is to evaluate the above regression results in terms of the signs of the coefficients, the statistical significance of the coefficients, and the explanatory power of the regression R2). The number in parentheses below the estimated slope coefficients refer to the estimated t values. The rule of thumb for testing the significance of the coefficients is if the absolute t value is greater than 2, the coefficient is significant, which means the coefficient is significantly different from 0. For example, the absolute t value for Px is 5.12, which is greater than 2; therefore, the coefficient of Px, (-9.50) is significant. In other words, Px does affect Qx. If the price of the commodity X increases by $1, the quantity demand (Qx) will decrease bu 9.50 units.

(c) Are X and Z complements or substitutes?