Consumer and producer surplus problem?

Question

Hello,

If a product costs $80, but the new supply and demand formulas are calculated to be Qd=175-P and Qs=2P-200, what is the consumer surplus, and producer surplus?

My equilibrium price came out to be 125 with 50 units.

Thank you in advance.

Answer 1

Equilibrium:

175-P=2P-200

3P=375

P=125

Q=50

Demand ans supply are linear

Supply: Q=0 P=100

Demand: Q=0 P=175

Consumer surplus (area below demand and above equilibrium price) =

= (175-125)*50/2=50*25=1250

Producer surplus (area of triangle above supply curve and below equilibrium price) =

=(125-100)*50/2=625

http://upload.wikimedia.org/wikipedia/en...

Total surplus (area between demand and supply curve equilibrium price) =

= (175-100)*50/2=75*25=1'875

P.S. Goofed my math a bit first time - thanks Dana Jaan for corrections. ;)

Answer 2

175-P=2P-200

375=3P

P=125

175-125=50

Yes, your price and quantity are correct.

Now, to find the consumer and producer surplus, take the area of the triangles above and below the line.  It will help a lot if you would draw a graph of this.

Consumer surplus:

First find the inverse demand curve.  This will tell you where the demand curve hits the y axis.

Q=175-P

P=175-Q

So the y intercept is 175.  Now since you know that price is 125 and quantity is 50, you can find the lengths of the sides of the triangle.  On the price side: 175-125=50

On the quantity side: 50-0=50

Find the area of the triangle:

50*50/2=1250

That's the consumer surplus.

Now for the producer surplus:

Find the inverse supply curve

Q=2P-200

Q+200=2P

P=Q/2+100

Now find the lengths of the sides of the triangle:

125-100=25

50-0=50

25*50/2=625

and that's the producer surplus