A linear industry demand function of the form Q = a + bP + cM + dP R were estima

Question

A linear industry demand function of the form   Q = a + bP + cM + dPR    were estimated using regress analysis. The results of this estimation are as follows:

DEPENDENT VARIABLE : Q R- SQUARE        F-RATIO               P-VALUE ON F

OBSERVATIONS: 24                                        0.8118                   28.75                     0.0001

VARIABLE            PARAMETER                       STANDARD

                                ESTIMATE                            ERROR                  T-RATIO               P-VALUE

INTERCEPT   68.38 12.65                     5.41                        0.0001

P                             -6.50                                      3.15 -2.06                      0.0492

M                            0.13926   0.0131                   10.63 0.0001

PR                           -10.77                                    2.45                        -4.40                      0.0002

a. Is the sign of b as would be predicted theoretically? Why?

b. What does the sign c of imply about the good?

c. What does the sign of d imply about the relation between the commodity and the related good R?

d. Are the parameter estimates, a, b, c, and d statistically significant at the 5 percent level of significance?

e. Using the values P = 225, M= 24,000, and PR = 60, calculate estimates of

                (1) The price elasticity of demand (E)

                (2) The income elasticity of demand (EM)

                (3) The cross-price elasticity (EXR)

Note: I could not recreate the ^ over b and d

Explanation / Answer

a. Yes, the sign of b is consistent with the theory. The law of demand states an inverse relationship between P and Q and the negative sign of b confirms such an inverse relationship through regression.

b. c is positive which means that the good is a normal good, that is, as the income goes up the demand for the good goes up.

c. The sign of d is negative which means that when the price of related good goes down the demand for the good goes up. Hence, the good and the related good are compliments.

d. As the p-value of all the variables corresponding to a, b, c and d is less than 0.05, all are significant at 5%.

e. First lets find Q at the given level. Q = a + bP + cM +dPr = 68.38 - 6.5*225 + 0.13926*24000 - 10.8*60 = 1301.92

(1) Price elasticity of demand = (P/Q)(dQ/dP) = (225/1301.92)*b = (225/1301.92)*(-6.50) = -1.12334

(2) Income elasticity of demand = (M/Q)(dQ/dM) = (24000/1301.92)*c = (24000/1301.92)*0.13926 = 2.56716

(3) Cross price elasticity = (Pr/Q)(dQ/dPr) = (60/1301.92)*d = (60/1301.92)*(-10.8) = -0.49634

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