The Instigator
pincivma
Pro (for)
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The Contender
dukula
Con (against)
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Demand equation with many variables and finding Profit maximization

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Voting Style: Open Point System: 7 Point
Started: 2/27/2016 Category: Economics
Updated: 1 year ago Status: Post Voting Period
Viewed: 329 times Debate No: 87341
Debate Rounds (5)
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pincivma

Pro

This is not really an argument but a way of finding out how to maximize profits. Here is my problem. I have run a regression for a hypothetical business to find out its demand equation. I ran a linear relationship for the last 10 years. Quantity is a function of price, consumer disposable income, and population.

Q = a + bP+ cI + d Pop where a is the intercept and b,c and d are the coefficients
Q is the quantity demanded P is the price, I is the disposable income and Pop is the population

After running the regression here is my demand equation
Q = -125 + 7.31P + .0030I + .0003Pop

Now I know that price does not shift the demand curve but Income and population shift it to the right. I also know that for profit maximization MR = MC. In this case MC = 2.

How do I find the MR of the demand equation above. It would be a very simple calculation using calculus if Price was the only variable but that is not realistic or the case here. Does any one out there have any suggestions??
dukula

Con

This is no opinion, no facts : this is just a question.. Debates??? I will keep my points for later... I assume Round 1 is for acceptance
Debate Round No. 1
pincivma

Pro

I made a small error. The plus sign should be a minus sign for the price. Q = -125 - 7.31P + .0030I + .0003Pop. I believe that once the regression is run for say data for a ten year period, take the current values of the explanatory variables except for the price variable and solving the equation for the price, you will then get an equation like this

P = a-bQ where "P" is the price and "Q" is the quantity. "a" is the P intercept and "b" is the slope. If you have a marginal cost of say "c" then the price that maximizes the demand equation is this

P = a -[(a-c)/2]. In other words all you need to find price that maximizes profits is the P intercept (i.e. the price that demands a zero quantity) and the marginal cost and that is it. Do you agree or disagree with this argument.

The equation P = a -[(a-c)/2] is derived by using calculus (MR = MC)
dukula

Con

Try googling your error. There are many websites which may help your matter dear friend
Debate Round No. 2
pincivma

Pro

I have no other argument unless someone out there can challang my lat post
Debate Round No. 3
pincivma

Pro

pincivma forfeited this round.
dukula

Con

dukula forfeited this round.
Debate Round No. 4
pincivma

Pro

pincivma forfeited this round.
dukula

Con

dukula forfeited this round.
Debate Round No. 5
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