Estimate an empirical demand function

Topics: Supply and demand, Consumer theory, Price elasticity of demand Pages: 3 (543 words) Published: October 7, 2014
1) Running regression analysis on data for 24 cities, Excel Data Analysis output is Regression Statistics
Multiple R0.9693
R Square0.9396
Adjusted R Square0.9306
Standard Error188.2038
Observations24

ANOVA
dfSSMSFSignificance F
Regression3110229603674320103.732.3E-12
Residual2070841435420.68
Total2311731374

CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept2308.5219.999610.49331.4E-091849.6182767.440
Price(P)-49.063.2748-14.98092.46E-12-55.891-42.229
Income(M)0.0703800.004416.07786.65E-130.0610.080
Population(N)0.0336360.00615.46952.36E-050.0210.046

As indicated by p-value of coefficients, all of them are significant. Therefore, demand function can be written as

Q = 2308.5 – 49.06*P + 0.07038*M + 0.033636*N

2) Demand function has coefficient of price as -49.06, meaning every increase of $1 in membership price causes demanded quantity to fall by about 49. Coefficient of average income is 0.07038, meaning a rise of $1000 in average income leads to an increase of about 70 in quantity demanded. Coefficient of population is 0.033636, meaning for every increase of 1000 in population, demanded quantity increases by about 34.

3) For town D, P = 63, Q = 3263, M = 45000
Point price elasticity of demand = (P/Q) dQ/dP = (63/3263)*(-49.06) = -0.947 Point income elasticity of demand = (M/Q) dQ/dM = (45000/3263)*(0.07038) = 0.971

4) As only costs are the fixed costs, profit is maximized when revenue (=PQ) is maximum. Revenue is maximized when marginal revenue becomes 0. Meaning at, d/dP (PQ) = 0
Or, d/dP (P*(2308.5 – 49.06*P + 0.07038*M + 0.033636*N)) = 0 Or, 2308.5 – 98.12*P + 0.07038*M + 0.033636*N = 0
Or, P = (2308.5 + 0.07038*M + 0.033636*N)/98.12

For town H, M = 41000, N = 28000, giving P = (2308.5+0.07038*41000+0.033636*28000)/98.12 = $62.53 For town W, M = 24000, N= 24000, giving P =...
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