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# Studying the effect of changes in variables on sales

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You are the manager for Dunkin Donuts and know the following elasticities:
n= 1.5 nI = 1.2 nxy1 = 0.5 nxy2 = -0.5

n is the price elasticity of demand for Dunkin Donuts (DD) glazed doughnuts, nxy1 is the cross elasticity of demand between DD glazed doughnuts and Krispy Kreme (KK) glazed doughnuts, nxy2 is the cross elasticity of demand between DD glazed doughnuts and DD French Vanilla coffee, and nI is the income elasticity of DD glazed doughnuts.

a) If you want to increase your sales of glazed doughnuts by 30%, in what direction and by how much do you need to change the price?

b) If you make the percentage price change that you calculated in part a) will total revenue increase or decrease? How do you know?

c) Krispy Kreme lowers its price of glazed doughnuts by 20%. The demand for Dunkin Donuts glazed doughnuts will change by what percentage and in what direction?

d) Dunkin Donuts raises the price of its French Vanilla coffee by 15%. The demand for Dunkin Donuts glazed doughnuts will change by what percentage and in what direction?

e) If average income increases by 5% by what percentage and in what direction will the demand for Dunkin Donuts glazed doughnuts change? Are DD glazed doughnuts a normal good or an inferior good and how do you know?

https://brainmass.com/economics/elasticity/studying-effect-changes-variables-sales-468781

#### Solution Preview

Please refer to the attached file for better formatting.

a) If you want to increase your sales of glazed doughnuts by 30%, in what direction and by how much do you need to change the price?

Since price and quantity demanded have inverse relationship. Price should be decreased to boost the sales.

% change in price=% change in sales/price elasticity of demand (?)
= 30%/1.5
=20%

Price should be decreased by 20%.

b) If you make the percentage price change that you calculated in part a) will total revenue increase or decrease? How do you ...

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## Lenny's, a national restaurant chain, conducted a study of the factors affecting demand (sales).

Lenny's, a national restaurant chain, conducted a study of the factors affecting demand (sales). The following variables were defined and measured for a random sample of 30 of its restaurants:
(NOTE: This question and the 3 that follow it, may require the use of statistical tables.)
---Y = Annual restautant sales (\$000)
---X1 = Disposable personal income (per capita) of residents within a 5 mile radius
---X2 = License to sell beer/wine (0=No, 1=Yes)
---X3 = Location (within one-half mile of interstate highway; 0 = No, 1 = Yes)
---X4 = Population (within a 5 mile radius)
---X5 = Number of competing restaurants within a 2 mile radius.

The data were entered into a computerized regression program and the following results were obtained:

MULTIPLE R ----------------------------.889
R-SQUARE ------------------------------.79
STD. ERROR OF EST. --------------.40

ANALYSIS OF VARIANCE

------------------------------DF--------------Sum of Squares--------------Mean Sqr.--------------F-Stat.
Regression --------------5--------------------326.13--------------------------65.226-----------------18.17
Error ----------------------24 --------------------86.17---------------------------3.590
Total ----------------------29 ------------------412.30

Variable--------------Coefficient--------------Std. Error--------------t-value
Constant__________.363____________.196___________1.852
__X-1____________.00275___________.00104_________2.644
__X-2 ____________76.65 ___________93.70 _________.818
__X-3 ____________164.3 ___________235.4_________ .698
__X-4 ____________.00331 __________.00126 ________2.627
__X-5 ____________-46.2 ____________12.1 _________-3.818

Based on the information presented above, which of the coefficients are statistically significantly different from zero at the .05 level of significance?

a. Constant, X-2 and X-3
b. X-1, X-4 and X-5
c. All except X-2 and X-3
d. None are significant

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