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Calculating Various Elasticity Values

You are the specific-area sales manager for a national company that provides, among other things, cable television service. Using monthly data for the number of subscriptions, prices, incomes, and prices of related goods for two full years (i.e., 24 months), you estimate demand for your company's high-definition television (HDTV) signal subscriptions with the following specification:

Q = a + bP + cM + dPR1 + fPR2, where:

Q is number of monthly subscriptions to your HDTV service
P is your company's monthly price for HDTV service;
M is average monthly income of people within the D.C. area;
PR1 is the price of related good 1;
PR2 is the price of related good 2.

The demand estimation results are as follows:

PARAMETER STANDARD
VARIABLE ESTIMATE ERROR
Intercept 250.0 22.5
P -10.0 -3.3
M 3.5 1.19
PR1 1.5 0.52
PR2 -4.5 -1.45

With current values of P=$60; M=$5,000; PR1=$50; PR2=$300, calculate:

i. The price elasticity of demand
ii. he income elasticity of demand
iii. The cross-price elasticity of demand with respect to related good 1
iv. The cross-price elasticity of demand with respect to related good 2.

Solution Preview

Regression equation is given by
Q=250.0-10P+3.5M+1.5PR1-4.5PR2

Put P=$60; M=$5,000; PR1=$50; PR2=$300
Q=250-10*60+3.5*5000+1.5*50-4.5*300=15875

i. The price elasticity of demand

Price elasticity of demand =(dQ/dP)*(P/Q)
Q=250.0-10P+3.5M+1.5PR1-4.5PR2
dQ/dP=-10

Given P=$60
Q=15875 (as calculated above)

Price elasticity ...

Solution Summary

Solution describes the steps to calculate price, income and cross price elasticity values in the given case.

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