20 Oligopoly Exercise

# 20 Oligopoly Exercise - SUMMARY OUTPUT Regression...

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SUMMARY OUTPUT Regression Statistics Multiple R 0.53 R Square 0.28 Adjusted R Square 0.28 Standard Error 2.52 Observations 392 ANOVA df SS MS F Significance F Regression 2 978.54 489.27 76.94 0 Residual 389 2473.74 6.36 Total 391 3452.28 Coefficients Standard Error t Stat P-value Lower 95% Intercept -0.7 2.12 -0.33 0.74 -4.87 SC Price -2.16 0.62 -3.47 0 -3.38 HY Price 5.57 1.6 3.47 0 2.42 qsc=-0.70-2.16Psc+5.57Phy Qsc = a + B1*Psc + B2*Phy

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Upper 95% Lower 95.0% Upper 95.0% 3.46 -4.87 3.46 -0.93 -3.38 -0.93 8.72 2.42 8.72
SUMMARY OUTPUT Regression Statistics Multiple R 0.31 R Square 0.1 Adjusted R 0.09 Standard E 2.15 Observation 392 ANOVA df SS MS F ignificance F Regression 2 194.44 97.22 21.04 0 Residual 389 1797.56 4.62 Total 391 1992 Coefficientstandard Erro t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% Intercept 4.57 1.81 2.53 0.01 1.02 8.12 1.02 8.12 SC Price 0.55 0.53 1.04 0.3 -0.49 1.6 -0.49 1.6 HY Price -3.5 1.37 -2.56 0.01 -6.18 -0.81 -6.18 -0.81 Qhy=4.57-3.50Phy+.55Psc qsc=-0.70-2.16Psc+5.57Phy

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Oligopolistic Pricing Exercise (Differentiated Bertrand Pricing) In this exercise you will find optimal pricing strategies for Hogi Yogi and Smart Cookie, two local competitors You will use data from a demand survey to construct demand curves for each firm's sandwich product. Usin information, you will find each firm's reaction function. A reaction function specifies a firm's profit maximizing price. You will then solve these equations simultaneously to identify the unique Bertrand-Nash equilibrium in that the players should charge to maximize profits. (Please refer to the Rivalry in Oligopoly reading for a full QUESTIONS 1. Using data from the survey below and Excel's regression feature, estimate the demand curve for e Smart Cookie Qsc=-0.70-2.16Psc+5.57Phy Hogi yogi Qhy=4.57-3.50Phy+.55Psc (Please note: Average cost for SC and HY will be given in Step 5 below) According to #5 According to data HY 1.45 HY 0.97 SC 0.46 SC 1 Psc-C)*Qsc = Profit, where C is average unit cost Profit SC Profit=(Psc-Csc)(-.7-2.16Psc+5.57Phy) HY Profit=(Phy-Chy)(4.57-3.5Phy+5.57sc) SC (Psc-.46)(-.7-2.16Psc+5.57Phy) HY (Phy-1.45)(4.57-3.5Phy+5.57sc) 3. Now (partially differentiate or use spreadsheet methods to) find the Psc and Phy, respectively, tha Solve for Psc and Phy, but leave these as variables for now. These are the reaction functions, which repr strategy for each firm. 4. If you did Steps 1, 2 and 3 correctly, you should have reaction functions as follows: inverted Psc= (.16-.23+Phy)/1.29 5. Now assume that the average cost for Hogi Yogi is \$1.45 for an ice cream cookie and, given its gr is \$0.46. Plot the reaction functions in Psc, Phy space. They should cross at the mutual best response pr Price Price (hy) Price (sc) \$0.50 \$1.42 \$0.33 \$1.00 \$1.46 \$0.72 \$1.50 \$1.50 \$1.11 \$2.00 \$1.54 \$1.50 \$2.50 \$1.58 \$1.88 \$3.00 \$1.62 \$2.27 \$3.50 \$1.66 \$2.66 \$4.00 \$1.70 \$3.05 (Hint: Use prices to predict a firm's demand; e.g. demand is of the form: Qsc = a + B1*P sc + B2*P hy ) For f 2. Now convert the demand function to a profit function for each firm. Do this by observing that (P
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20 Oligopoly Exercise - SUMMARY OUTPUT Regression...

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