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MANAGERIAL ECONOMICS 12th Edition By Mark Hirschey Demand Estimation Chapter 5 Chapter 5 OVERVIEW • • • • • • • Interview and Experimental Methods Simple Demand Curve Estimation Simple Market Demand Curve Estimation Identification Problem Regression Analysis Measuring Regression Model Significance Measures of Individual Variable Significance Interview and Experimental Methods Consumer Interviews Interviews can solicit useful information when market data is scarce. Consumer opinions can differ from behavior. Market Experiments Controlled experiments can generate useful insight. Experiments can be expensive. Simple Demand Curve Estimation • Simple Linear Demand Curves • • • The best estimation method balances marginal costs and marginal benefits. Simple linear relations are often useful for demand estimation. Using Simple Linear Demand Curves • Straight-line relations can give useful approximations. Simple Demand Curve Estimation Consider the linear demand: = + when P=$12, Q=3,200 and P=$10, Q=4,000 12 = + 3200 minus 10 = + 4000 2 = −800 b = −0.0025 = + is 12 = + 3200 12 = − 0.0025 3200 12 = − 8 = 20 = 20 − 0.0025 Demand Curve and TR Maximization = ∙ = $20 − $0.0025 = $20 − $0.0025 2 = = $20 − $0.005 $20 − $0.005 = 0 $0.005 = $20 = 4000 and = 20 − 0.0025 4000 = $10 max = ∙ = 4000 ∙ $10 = $40,000 Market Demand Curve Estimation Market Demand Curve Shows total quantity customers are willing to buy at various prices under current market conditions. Graphing the Market Demand Curve Market demand is the sum of individual demand quantities, Q1 + Q2 = Q1+2. Add quantities, not prices! Market Demand Curve Estimation = $100 − $0.001 = $80 − $0.004 Domestic Demand Foreign Demand = $1,200,000 + $24 Total Cost = $100 − $0.001 = $80 − $0.004 0.001 = 100 − 0.004 = 80 − = 100,000 − 1000 = 20,000 − 250 Market Demand Curve Estimation = + = 100,000 − 1000 + 20,000 − 250 = 120,000 − 1,250 1,250 = 120,000 − = $96 − $0.0008 Market Demand Market Demand Curve Estimation = ∙ = $96 − $0.0008 = $96 − $0.0008 2 = = $96 − $0.0016 = $1,200,000 + $24 = = $24 Market Demand Curve Estimation = at profit maximization $96 − $0.0016 = $24 $0.0016 = $72 = 45,000 = $96 − $0.0008 45,000 = $60 = − = $96 − $0.0008 2 − ($1,200,000 + $24) = −$0.0008 2 + $72 − $1,200,000 = −$0.0008 45,000 = $420,000 2 + $72 45,000 − $1,200,000 Market Demand Curve Estimation $120 $100 $80 $60 $40 Domestic Demand $20 Market Demand Foreign Demand $0 0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 Identification Problem • Changing Nature of Demand Relations • • Interplay of Demand and Supply • • Economic conditions affect demand and supply. Shifts in Demand and Supply • • Demand relations are dynamic. Curve shifts can be estimated. Simultaneous Relations • Quantity and price are jointly determined. Identification Problem The demand curve “D” does not exist the data are for three shifting demand curves All else equal w.r.t. demand determinants D1 S1 P S1 P D2 S2 P1 S2 The problem: “D” has higher elasticity than “D1”. P1 D3 S3 P2 S3 P2 P3 P3 D Q1 Q2 Q3 D Q Q1 Q2 Q3 Q Regression Analysis • What Is a Statistical Relation? • • • Specifying the Regression Model • • • A statistical relation exists metrics are related A deterministic relation is true by definition. Dependent variable Y is caused by X. X variables are independently determined from Y. Least Squares Method • Minimize sum of squared residuals. Regression Analysis Direct Relation Unit Sales Inverse Relation Unit Sales .... . . .... . Advertising X Unit Sales ... ... ... .. Price No Relation X .... ...... Orbit of Jupiter X Regression Analysis Y Regression Analysis fits a “Sum of Least Squares” line to the data − 2 Estimate or . . − = . . 2 − 2 . . . Error or − . Observation or − . = . . . = + = 0.136047 + 0.005962 X Regression Analysis 24 43 24 34 36 38 22 23 30 33 = = 78 100 86 82 86 84 75 80 83 91 1872 4300 2064 2788 3096 3192 1650 1840 2490 3003 2 576 1849 576 1156 1296 1444 484 529 900 1089 − 2 − − 2 79.50 93.67 79.50 86.96 88.45 89.94 78.01 78.76 83.98 86.21 -1.50 6.33 6.50 -4.96 -2.45 -5.94 -3.01 1.24 -0.98 4.79 105 100 95 90 85 80 75 70 65 10 20 30 10 26295 − 307 845 = = 0.745623 10 9899 − 307 2 856 − 0.745623 ∙ 307 = = 61.60937 10 = 61.60937 + 0.745623 40 50 Regression Analysis Regression equations can take on any functional form = + = + + + = 0 The above multiplicative form is popular among economist because the exponents “bP” is the constant elasticity of the variable. = 4−0.4 0.2 0.003 has the constant price elasticity of – 0.4 Measuring Regression Significance Standard Error of the Estimate (SEE) reflects degree of scatter about the regression line. Y Upper 95% confidence bound: + 1.96 standard error of the estimate = + = Slope of curve Lower 95% confidence bound: - 1.96 standard error of the estimate X Goodness of Fit • Correlation shows degree of concurrence. • • • Coefficient of determination, R2. • • • r = 1 means perfect correlation. r = 0 means no correlation. R2 = 100% means perfect fit. R2 = 0% means no relation. Corrected coefficient of determination • Adjusts R2 downward for small samples. Regression Analysis Regression Analysis fits a “Sum of Least Squares” line to the data 2 = Y Total variation − − − 2 2 Unexplained variation − Explained variation − − 2 = 1 − (1 − 2 ) X −1 −−1 F statistic Tells if R2 is statistically significant Goodness of Fit Test Do not Reject H0 Reject H0 F = 0.05 = 0.1 F = 2.69 F = 2.14 Critical Value Judging Variable Significance • t statistics compare sample characteristics to the standard deviation of that characteristic. • • • Two-tail t Tests • • t > 1.645 implies a strong effect of X on Y (90% conf.). t > 1.96 implies an even stronger effect of X on Y (95% conf.) Tests of effect. One-Tail t Tests • Tests of magnitude or direction. Judging Variable Significance t – statistic H0: b=0 Ha: b≠0 Reject H0 Reject H0 / 2 = 0.025 – 1.96 Do not Reject H0 0 / 2 = 0.025 1.96 z Confidence Level = 95% / 2 = 0.025 Critical Value = ± 1.96 / 2 = 0.05 Critical Value = ± 1.645 Confidence Level = 90% Multiple Regression Example SUMMARY OUTPUT Regression Statistics Multiple R 0.939811 R Square 0.883244 Adjusted R Square 0.836542 Standard Error 2.929296 Observatio ns 15 ANOVA df Regression Residual Total SS MS F Significanc eF 4 649.1256 162.2814 18.91221 0.000118 10 85.80775 8.580775 14 734.9333 Coefficient s Intercept 23.30213 P -5.96115 Ps 6.50636 Pc -1.09766 I -1.3E-05 Standard Error 17.55563 2.928719 3.888925 3.416276 0.000116 t Stat 1.327331 -2.03541 1.673049 -0.3213 -0.10919 P-value Lower 95% 0.213904 -15.8142 0.069176 -12.4867 0.125263 -2.1587 0.754595 -8.7096 0.915211 -0.00027 Q 20 30 10 15 12 28 17 14 20 22 32 14 25 28 12 P 2 1.5 2.3 2.5 2.8 1.7 2.4 3 2 2 1.4 3 1.8 1.6 3 Upper Lower Upper 95% 95.0% 95.0% 62.41851 -15.8142 62.41851 0.564444 -12.4867 0.564444 15.17142 -2.1587 15.17142 6.514275 -8.7096 6.514275 0.000245 -0.00027 0.000245 Ps 1.5 2.5 1.7 1.9 1.4 2.7 1.8 1.7 2.1 2.3 2.8 1.4 2.4 2.6 1.7 Pc 3 2.3 3.2 2.8 3.5 2.2 3.1 3.8 2.9 2.3 2.4 3.1 2.4 2.2 3.1 I 38000 22000 40000 25000 28000 17000 35000 40000 20000 34000 20000 40000 36000 36000 30000