# Is this good a substitute or complement with respect to related good R?

s Country Mart where Q i Show more onsider the following nonlinear (multiplicative) demand function for Kelleys Country Mart where Q is the quantity of the product sold P is the price of product M is the average income of the household in Emporia and PR is the price of related goods (R). The method of least-squares is used to estimate the parameters. Q = aPb M c Pd R The results of the estimation are: DEPENDENT VARIABLE: LNQ R-SQUARE OBSERVATIONS: 26 0.9248 F-RATIO P-VALUE ON F 90.18 0.0001 PARAMETER STANDARD VARIABLE ESTIMATE INTERCEPT 3.04 LNP 1.90 LNM 2.16 LNPR 0.78 ERROR T-RATIO 1.01 3.01 0.48 3.96 0.675 3.20 0.169 4.62 P-VALUE 0.0064 0.0007 0.0041 0.0001 a. Before the nonlinear demand equation can be estimated using regression analysis the demand equation must be transformed into a log-linear form. Write the equation with t- stat R2 F-stat information. b. Are the slope parameter estimates statistically significant at the 5 percent level of significance? c. Estimated value of a the intercept? d. Is this good a normal or inferior good? e. Is this good a substitute or complement with respect to related good R? f. Compute estimates of the following elasticities: (i) Thepriceelasticityofdemand. (ii) The income elasticity of demand. (iii) The cross-price elasticity of demand. g. For a 23.15 percent decrease in household income holding all other things constant what will happen to quantity demand for the good? h. All else constant a 4 percent increase in price of the good will cause what percentage increase or decrease in the quantity sold of the good? i. A 12.82 percent decrease in the price of R holding all other things constant will cause what percent change in the quantity demanded of the good? Show less

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