7Demand Analysis Solutions

Q UESTION 1Completed in classQUESTION 2(i)Log (P x) represents the price elasticity of cigarettes, as variables transformed into logsare expressed as percentages.If cigarette prices increased by 20 percent, holding all other variables constant, quantity demand would decrease by 8.35%.(ii)It is considered to be a inferior good as it is negative, however looking at the size of the coefficient, it can be noted that it is quite small and close to zero. So although it is considered to be an inferior good and as a result is quite sensitive to income, the proximity of the coefficient to 0 would suggest that it is not as sensitive to income as some other inferior goods could be.(iii)H0: b = 0H a: b ≠ 0T-statisticsLog(P x): -2.0714 > 2.045 => SignificantLog (A x): 4 > 2.045 => SignificantLog I: -1 < 2.045 => InsignificantLog P c: 0.9333 < 2.045 => InsignificantC: -5.2632 > 2.045 => SignificantD: -3.529 > 2.045 => Significant{Conclude in same format as above question}The overall significance of the model if tested using the F-test:H0 : b1 = b2 = b3 = b4 = b5 = b6 = 0H a: At least one of the b’s are not equal to zeroF-statistic = 75.68F-critical value = 2.43As the f-statistic of 75.68 exceeds the f-critical value of 2.43 with 6 degrees of freedom in the numerator and 29 degrees of freedom in the denominator, we can reject the null hypothesis at the 5% significance level and conclude that at least one of the b’s does not equal zero and so as a result the model is statistically significant overall.QUESTION 3(i)Q d = 40 – 11,250 + 5,040 + 12,000 + 46,400 + 696 – 2,480 = 50,446Elasticities:Price: -0.22 => Inelastic demand: any percentage increase in price will result in a smaller decrease in the quantity demanded.Cross Price: 0.09 => coefficient is positive => substitute but is quite low so is not much of a substitute for raingear, which suggests that Raingear could be a differentiated product from that of its competitor. Perhaps it might be worth including a variable for umbrellas to test if it is a viable substitute for raingear – this model could have included the wrong substitute. WE would expect a higher cross price elasticity if the two goods were substitutes.Income: 0.29 => positive – normal good. As it is less than 1 however, it is a necessity. The value is quite low, thus an increase in income will lead to a very small percentage increase in the quantity demanded of raingear.Advertising: 0.92 => quite a high elasticity. Generally an advertising elasticity of 1 (or close to 1) would encourage the firm to spend more on advertising. High advertising elasticity suggests an increase in advertising will lead to increase quantity demanded. This means the company should focus on advertising the product as any increased expenditure on advertising will increase quantity demanded. One suggestion would be to market the product as a differentiated one. This is supported by the cross price elasticity as the brand of competing rainwear does not appear to be a substitute.Holidays: -0.05 => Inelastic demand: Number of foreign holidays taken does not affect quantity demanded of raingear. We would expect this as Irish people usually take sun/snow holidays. This poses the question, do we need to include this variable?The R-squared is 0.62 which is not that strong. This is interpreted as 62% of the variation in quantity demanded is explained by the independent variables in the model. This suggests that variables do not adequately measure the variance in the quantity demanded of raingear. Other variables which could be included would be:Price of umbrellas as a substitute for raingear.Number of holidays Irish people take in Ireland every year (weekend breaks etc).Number of foreign visitors who holiday in Ireland each yearLimited distribution channels?Possible complementsGovernment regulationsCompetitionBarriers to entryDominant playerMarket share variable(ii)N = 6 * 16 * 26 = 2496N – K = 2496 – 7 = 2489H0: b = 0H a: b ≠ 0t-statistic:P = -6.25 > 1.96P x = 4.14 > 1.96I = 2.76 > 1.96A = 4.83 > 1.96W = 1.90 < 1.96H = -1.25 < 1.96Therefore we have four strongly significant variables so any policy decisions made on these variables are suitable and still stand.The overall significance of the model if tested using the F-test:H0 : b1 = b2 = b3 = b4 = b5 = b6 = 0H a: At least one of the b’s are not equal to zeroF-statistic = 676.933F-critical value = 2.10As the f-statistic of 676.933 exceeds the f-critical value of 2.10 with 6 degrees of freedom in the numerator and 2489 degrees of freedom in the denominator, we can reject the null hypothesis at the 5% significance level and conclude that at least one of the b’s does not equal zero and so as a result the model is statistically significant overall. (iii)95% Confidence interval: 50,446 ± 1.96(5.91) = 50,446 ± 11.5836SAMPLE QUESTION A14(i)Q d = 54,797.5E P = -0.007 => InelasticE A = 0.09 => Inelastic (weak)E px = 0.0038 => substitute (weak)E Y = 0.662 => normal good which is a necessityE pop = 0.228 => inelasticPolicy implications:Advertising elasticity is quite low- Not a strong brand-Standardised product-Need to differentiate product moreAdvertising and cross price elasticities seem to contradict each other-Could be that we’re including the wrong competitor-Company could be the dominant firm in industry-Barriers to entry in the industryPossible scenarios1.Strategy must be directed to reinforce barriers or differentiate product more2.Targeted advertising – may be using wrong medium, wrong target etc.Missing variables:Price of fresh vegetablesMarket share variable(ii)H0: b = 0H a: b ≠ 0Look up t tables: Tcrit = 2.021T-statistics•P: 275/52 = 5.29 > 2.021 [significant]•A: 5/1.1 = 4.55 > 2.021 [significant]•Px: 150/66 = 2.27 > 2.021 [significant]•Y: 7.25/3.2 = 2.27 > 2.021 [significant]•Pop: 0.25/0.09 = 2.78 > 2.021 [significant]•T: 875/230 = 3.80 > 2.021 [significant]Therefore, all variables are significant.(iii)Q = -500 – 275(1.50) + 5(1000) + 150(1.40) + 7.25(5000) + 0.25(50000) + 875(5) Q = - 500 – 412.50 + 5000 + 210.00 + 36250 + 12500 + 4375Q = 57,422.5C.I.: Q + tcrit*S.E.E.C.I. = 54,797.5 + 2.021* 775。