Please answer the following questions using equations for a supply and demand curve. In a perfect market the supply curve is Qs=9p and the demand curve is Qd=100-p. a) find the market equilibrium...

Please answer the following questions using equations for a supply and demand curve.

In a perfect market the supply curve is Qs=9p and the demand curve is Qd=100-p.

a) find the market equilibrium price

b) find the market equilibrium quantity 

b) Calculate the consumer surplus

c) Calculate the producer surplus

d) What happen if the state decide to fix a minimum price of 8?

e) How much will be the loss in efficiency due to the government intervention?

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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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To find the equilibrium price and quantity, we simply set the equations for the demand curve and the supply curve to be equal to one another and then solve for P.  That will tell us the equilibrium price:

9P = 100 – P

100 = 10P

P = 10

Equilibrium price is 10.

To find the equilibrium quantity, we now plug the price back into one or both of the equations for the demand and supply curve.  The answer will be the same for either equation.

Q = 9(10) or Q = 100 – 10.

In either case, Q = 90.

Equilibrium quantity is 90.

To find the consumer surplus, we find the area of a triangle whose vertices are the equilibrium price on the y-axis, the equilibrium quantity at the equilibrium price, and the price at which quantity demanded is zero.  Please follow the link below to see this done in graphic form.

First, we must find the price at which quantity demanded is zero.  We set Q equal to 0 and solve for P.

0 = 100 – P

P = 100.

We now use the formula for the area of a triangle, which is Area = ½ (base*height).

Consumer surplus = ½ [(100-10)*90]

= ½ (90*90)

= 4050

Consumer surplus is 4050.

To find the producer surplus, we do the same calculation, only this time the triangle’s vertices are the equilibrium price on the y-axis, the equilibrium quantity at the equilibrium price, and the price at which quantity supplied is zero.

First, we must find the price at which quantity supplied is zero.  We set Q equal to 0 and solve for P.

0 = 9P

P = 0

Using that result to find the area of the triangle:

Producer surplus = ½ [(10-0)*90]

= ½ (10*90)

= 450

Producer surplus is 450.

In your question, you ask what will happen if the state sets a minimum price of 8. In this situation, there will be no change from the natural equilibrium.  This is because the price floor is set lower than the equilibrium price.  Producers will not be required to lower their prices because the price of 8 is a minimum and not a maximum. 

If the government sets a minimum price of 8, nothing will happen and there will be no loss of efficiency.

The answers to your questions, then, are:

A: Equilibrium price is 10.

B: Equilibrium quantity is 90.

C: Consumer surplus is 4050.

D: Producer surplus is 450.

E and F: If the government sets a minimum price of 8, nothing will happen and there will be no loss of efficiency

Sources:

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