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# 8. 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

8. 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 recreational areas −1.02 1.06
Highway construction and −1.09 0.99
maintenance

(a) Do these public goods conform to the law of demand? For which public goods is demand price elastic? (b) What types of goods are these public goods? (c) If the price or cost of college and university education increased by 10 percent and, at the same time, incomes also increased by 10 percent, what would be the change in the demand for college and university education?

15. Integrating Problem Starting with the data for Problem 6 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 relabel Qˆ x), 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 get 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 1999 2000
Pz (\$) 20 19 21 21 22
Year 2001 2002 2003 2004 2005
Pz (\$) 23 23 24 25 25

Qˆx = 121.86 – 9.50Px + 0.04Y – 2.21Pz
(–5.12) (2.18) (–0.68)
R^2 = 0.9633 F = 167.33 D–W = 2.38

(a) Explain why you think we have chosen to include the price of commodity Z in the above regression. (b) Evaluate the above regression results. (c) Are X and Z complements or substitutes?

Notes:
1. P15(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 zero. For example, the absolute t value for Px is 5.12 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 demanded (Qx) will decrease by 9.50 units.
8. 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 recreational areas −1.02 1.06 Highway construction and −1.09 0.99 maintenance (a) Do these public goods conform to the law of demand? For which public goods is demand price elastic? (b) What types of goods are these public goods? (c) If the price or cost of college and university education increased by 10 percent and, at the same time, incomes also increased by 10 percent, what would be the change in the demand for college and university education? 15. Integrating Problem Starting with the data for Problem 6 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 relabel Qˆ x), 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 get 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 1999 2000 Pz (\$) 20 19 21 21 22 Year 2001 2002 2003 2004 2005 Pz (\$) 23 23 24 25 25
Qˆx = 121.86 – 9.50Px + 0.04Y – 2.21Pz (–5.12) (2.18) (–0.68) R^2 = 0.9633 F = 167.33 D–W = 2.38 (a) Explain why you think we have chosen to include the price of commodity Z in the above regression. (b) Evaluate the above regression results. (c) Are X and Z complements or substitutes? Notes: 1. P15(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 (R 2 ) 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 zero. For example, the absolute t value for Px is 5.12 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 demanded (Qx) will decrease by 9.50 units.

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15. Integrating Problem Starting with the data for Problem 6 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...

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