Question

Given the following data, find the Demand equation where P is the y variable, and Q...

Given the following data, find the Demand equation where P is the y variable, and Q is the x variable [P = f(Q)].

Q

P

180

475

590

400

430

450

250

550

275

575

720

375

660

375

490

450

700

400

210

500
  • Present the correspond equations for Total Revenue, and for Marginal Revenue.
Business   Economics   
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Answer #1

Regression Summary Output is as follows.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.8657
R Square 0.7495
Adjusted R Square 0.7182
Standard Error 37.4321
Observations 10
ANOVA
df SS MS F
Regression 1 33540.69576 33540.7 23.93775
Residual 8 11209.30424 1401.163
Total 9 44750
Coefficients Standard Error t Stat P-value
Intercept 585.0911 29.1051 20.1027 0.0000
Q -0.2888 0.0590 -4.8926 0.0012

Therefore:

(1) Demand equation: P = 585.0911 - 0.2888 x Q

(2) Total revenue (TR) = P x Q = 585.0911Q - 0.2888 x Q2

(3) Marginal revenue = dTR/dQ = 585.0911 - 0.5776 x Q

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