Question 5 Consumers have the option of dining on Checker’s Pizza. Alternatively

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Question 5

Consumers have the option of dining on Checker’s Pizza. Alternatively, they can dine on Al’s Pizza or a Big Mac. Given the latter two alternatives, use your elasticity calculations to determine which option consumers would choose, Al’s Pizza or the Big Mac. Be sure to explain your answer using economic theory.

Question 6

If expectations for next year are that all prices, that is P, PAL, and PBMAC, are all going to increase by 5%, and M INCOME is going to increase by 10%. What is your prediction for the percent change in the quantity demanded for Checker's Pizza? Use the elasticities you calculated in question 2 (above) to complete this question. Show all of your computational work.

Question 7

If the independent variables (P, M INCOME, PAL, and PBMAC) take on the values below, how many pizzas could Checker's expect to sell? Use your estimated equation to solve this problem.

            P = $11.50                                M INCOME = $35,000

            PAL = $10.00                PBMAC = $3.00

SUMMARY OUTPUT Regression Statistics Multiple R 0.97747728 R Square 0.955461832 Adjusted R Square 0.946085376 Standard Error 42.4112273 Observations 24 ANOVA df SS MS F Significance F Regression 4 733155.8015 183288.9504 101.9000984 1.46651E-12 Residual 19 34175.53183 1798.712201 Total 23 767331.3333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1183.802486 506.2980062 2.338153561 0.03046727 124.1085806 2243.496392 124.1085806 2243.496392 P -213.4219011 13.48631686 -15.82506946 2.13823E-12 -241.6490867 -185.1947155 -241.6490867 -185.1947155 M_INCOME 0.091088289 0.012409922 7.339956795 5.87592E-07 0.065114024 0.117062553 0.065114024 0.117062553 PAL 101.3028564 38.74776028 2.614418373 0.017051999 20.20286208 182.4028507 20.20286208 182.4028507 PBMAC 71.84479909 27.09970176 2.651128774 0.015762653 15.12447145 128.5651267 15.12447145 128.5651267 Demand Funcation: Q = a + bP + cM + dPal + ePBMac Q=1183.802486-213.4219011(9.5)+0.091088289(26614)+101.3028564(10.12)+71.84479909(1.15) 2688.324575 Q= 1183.802486 -2027.50806 2424.223723 1025.184907 82.62151895 2688.324575 Q=2688.324575 P M_INCOME PAL PBMAC Mean 9.04625 Mean 26613.20833 Mean 10.11875 Mean 1.145833333 Standard Error 0.196396719 Standard Error 201.0751264 Standard Error 0.049344664 Standard Error 0.076133742 Median 8.65 Median 26160 Median 10.175 Median 1.15 Mode 8.65 Mode 26120 Mode 10.25 Mode 0.55 Standard Deviation 0.962143497 Standard Deviation 985.0629192 Standard Deviation 0.241738495 Standard Deviation 0.372977639 Sample Variance 0.925720109 Sample Variance 970348.9547 Sample Variance 0.0584375 Sample Variance 0.139112319 Kurtosis -1.212342961 Kurtosis -0.666212905 Kurtosis 0.06932939 Kurtosis -0.307829156 Skewness -0.301450314 Skewness 0.902768178 Skewness -0.653503709 Skewness 0.021936167 Range 2.75 Range 3000 Range 0.95 Range 1.3 Minimum 7.5 Minimum 25500 Minimum 9.6 Minimum 0.55 Maximum 10.25 Maximum 28500 Maximum 10.55 Maximum 1.85 Sum 217.11 Sum 638717 Sum 242.85 Sum 27.5 Count 24 Count 24 Count 24 Count 24 Ê=^b(P/Q) -0.718167699 ÊM=(M/Q) 0.901733233 Ê=^d(PAL/Q) 0.381300044 ÊXBMAC=ê(PMAC/Q) 0.030622108

Explanation / Answer

Solution:

Clearly, given the t-Stats or p-values, we can see that all the explanatory variables, P, PAL, PBMAC and M_INCOME are statistically significant.

Q5) The elasticity values are found to be ePAL = 0.3813 and ePBMAC = 0.0306

This means that demand for Checker's Pizza is affected more by the prices of Al's Pizza as compared to the Big Mac (notice that elasticity is higher of Al Pizza). So, say the prices for Al Pizza reduce by 1%, this will reduce demand for Checker's Pizza by 0.38% while same 1% reduction in price of Big Mac, demand for Checker's Pizza will reduce by only 0.03%. Clearly, consumers are willing to substitute more towards Al Pizza than Big Mac, for Checker's Pizza.

So, consumers will choose Al's Pizza among the two alternatives.

Q6) Elasticity(Q,P) implies percentage change in the quantity demanded of Checker's Pizza, when Price of Chceker's Pizza change by 1%. (rest elasticities for PAL, PBMAC, M_INCOME are analogous to this).

So, using the elasticity valuations, we know that increase in P of 1% decreases Q by 0.718%. Increase in PAL, PBMAC and M_INCOME of 1%, increases Q by 0.38%1, 0.031%, and 0.902%, respectvely.

Hence, given that P, PPAL, and PBMAC each increase by 5%, expectedly and M_INCOME expectedly increase by 10%, expected change in Y (in percentage terms) =

Y^ = 5*(-0.718) + 10*0.902 + 5*0.381 + 5*0.031

Y^ = -3.59 + 9.02 + 1.905 + 0.155

Y^ = +7.49

So, quantity demanded for Checker's Pizza will increase by 7.49% (plus sign denotes increase)

Q7) We have the demand function as Q = 1183.802 - 213.422*P + 0.0911*M_INCOME + 101.303*PAL + 71.845*PBMAC

So, given that P = $11.50, M_INCOME = $35,000, PAL=$10.00, PBMAC = $3.00

So, Q = 1183.802 - 213.422*11.5 + 0.0911*35000 + 101.303*10 + 71.845*3

Q = 1183.802 - 2454.353 + 3188.5 + 1013.03 + 215.535

Q = 3146.514

So, Checker's expect to sell 3,147 pizzas approximately.

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