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December 6th, 2016, 06:43 PM   #1
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Consumers' and producers' surplus

Consumers' and producers' surplus

The quantity x demanded per week, in units of a hundred, of a certain product is related to the unit price p (in dollars) by the relation

p= −0.01x^2−0.4x+249

The quantity x, in units of a hundred, that the supplier is willing to make available in the market per week is related to the unit price p by the relation

p= 0.02x^2+0.1x+17

If the market price is set at the equilibrium price, find the consumer's surplus and the producers' surplus.
Simongekyo is offline  
December 6th, 2016, 07:42 PM   #2
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We tend not to give answers but rather help for what are obviously homework problems.

In this case, your problem is a bit unclear, probably because you paraphrased it. I am not sure what setting equilibrium price equal to market price is supposed to mean because in a functional, competitive market, the equilibrium price will be the market price. But ignoring that, your first task is to find that equilibrium price. How do you do that? What numeric result do you get for equilibrium price? What numeric result do you get for equilibrium quantity exchanged? This is basic supply and demand analysis.

Graphically, consumers' surplus is the area bounded by the y axis, the line parallel to the x axis with a y value equal to the equilibrium price, and the demand function. Producers' surplus is the area with what bounds? These are definitional issues.

The mathematical technique to find areas is what? Do you need help with setting up that technique?
JeffM1 is offline  
December 7th, 2016, 01:59 AM   #3
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Originally Posted by Simongekyo View Post
p = −0.01x^2−0.4x+249
p = 0.02x^2+0.1x+17
These equations give the same value of p for a particular positive value of x (which happens to be an integer). The equilibrium price mentioned in the question is probably intended to be that value of p.

I've moved this thread to the economics forum.
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