# In a study published in 1980, B. B. Gibson estimated the following price and income elasticities

Problem 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 ELASTICITYAid to needy people -0.83 0.26Pollution Control -0.99 0.77Colleges and universities -0.87 0.92Elementary school aid -1.16 1.14Parks and recreation areas -1.02 1.06 Highway construction and -1.09 0.99maintenanceDo these public goods conform to the law of demandProblem 15 (b):Integrating Problem Starting with the data:YEAR Y X1 X11986 72 \$10 \$2,0001987 81 9 2,1001988 90 10 2,2101989 99 9 2,3051990 108 8 2,4071991 126 7 2,5001992 117 7 2,6101993 117 9 2,6981994 135 6 2,8011995 135 6 2,9211996 144 6 3,0001997 180 4 3,0991998 162 5 3,2011999 171 4 3,3082000 153 5 3,3972001 180 4 3,5012002 171 5 3,6892003 180 4 3,8002004 198 4 3,8962005 189 4 3,989And 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 e 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 1990Pz (\$) 14 15 15 16 17YEAR 1991 1992 1993 1994 1995Pz (\$) 18 17 18 19 20YEAR 1996 1997 1998 1994 2000Pz 20 19 21 21 22YEAR 1996 1997 1998 1994 2000Pz 23 23 24 25 25Qx = 121.86 â 9.50Px + 0.04Y â 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?

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