Problems
3. (a) Starting with the estimated demand function for Chevrolets given in problem 2, assume that the average value of the independent variables changes to N=225 million, I=$12,000, P_{F}=$10,000, P_{G}=100cents, A=$250,000, and P_{I}=0 (i.e., the incentives are phased out). Find the equation of the new demand curve for Chevrolets. * Revised 3(b): If P_{c} is $10,000, find the value of Q_{c}.
Function from Problem 2 is:
Qc= 100,000-100Pc+ 2,000N + 50I + 30Pf – 1,000Pg +3A + 40,000Pi
7. The total operating revenue of a public transportation authority are $100 million while its total operating cost are $120 million. The price of a ride is $1, and the price elasticity of demand for public transportation has been estimated to be -.04. By law, the public transportation authority must take steps to eliminate its operating deficit. (a) is asking should the transportation authority increase or decrease the price per ride based upon the price elasticity of demand. (b) Use equation (3-7.) Suggestion: increase the price of a ride to be $1.50.
your situation, I’ll explain it briefly here.
14. Suppose that a firm maximizes its total profits and has a marginal cost (M/C) of production of $8 and the price elasticity of demand for the product sells is (-)3. Find the price at which the firm sells the product. *** Use equation (3-12) and to maximize the profits, MR has to equal MC.
Chapter 5
Discussion
15. Integrating Problem. Starting with the data for Problem 6 and the data on the price of a related commodity for year 1986 to 2005 given below, we estimated the regression for the quantity demanded for a commodity (which we now relabel Ô_{X}), on the price of the commodity (which we now relabel P_{X}), consumer income (which we now lable Y), and the price of the related commodity (P_{Z}), and we obtain the following results. (If you can, run this regression yourself; you should get results identical or very similar to those given below.
Year |
1986 |
1987 |
1988 |
1989 |
1990 |
Pz ($) |
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 |
Ô_{X }= 121.86-9.5P_{X}+0.04Y-2.21P_{Z}
(-5.12) (2.18) (-0.68)
R^{2}=0.9633 F= 167.33 D-W = 2.38
15(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 which is greater than 2, therefore, the coefficient of Px, (-9.50) is significant. In order 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.
15(c) X and Z are complementary or substitutes?