The demand curve for labor is  Q=100-5P. The supply curve is Q=5P. Helpful hint. The indirect (inverse) demand curve is P=20-0.2Q a) What is the equilibrium price and quantity. b) What is the...

The demand curve for labor is  Q=100-5P. The supply curve is Q=5P.

Helpful hint. The indirect (inverse) demand curve is P=20-0.2Q

a) What is the equilibrium price and quantity.

b) What is the consumer surplus?

c) What is the producer surplus?

d) What is the total surplus?

Expert Answers
pohnpei397 eNotes educator| Certified Educator

In order to answer these questions, we must do a bit of simple algebra. 

First, we will find the equilibrium price and quantity using the equations given.  The demand curve’s equation was Q = 100 – 5P and the supply curve’s equation was Q = 5P.  To find the equilibrium quantity, we set these equations to be equal to one another.  That gives us

100 – 5P = 5P

100 = 10P

P = 10

This means that the equilibrium price is $10.  Now that we have the equilibrium price, we can find the equilibrium quantity by plugging the price in to either of the demand or supply curve equations.

Q = 100 – 5(10) or Q = 5 (10)

Q = 100 – 50 = 50 or Q = 50

Whichever way we figure it, the equilibrium quantity is 50.

Now we need to figure the consumer surplus.  First, we find the y-intercept of the demand curve.  This is the price where the quantity demanded (Q) will be 0.  We do this using the equation for the demand curve. 

0 = 100 – 5P

-100 = -5P

20 = P

This tells us that consumers will buy zero hours of labor when the price is $20.  We can now use this to find the consumer surplus.  We can find the consumer surplus by finding the area of a triangle whose vertices are the equilibrium quantity, the maximum price (y-intercept of the demand curve) and the equilibrium price.  The formula for the area of a triangle is ½(b*h).

The base of the triangle is found by subtracting the equilibrium price from the maximum price.  In this case, that is 20 – 10  = 10.  The height of the triangle is found by finding how far the equilibrium quantity is from the y-axis (50).  To visualize this, please follow the link and scroll down to the graph.

Using the formula for the area of a triangle, we have

Consumer surplus = ½ (10*50)

= ½ (500)

= 250

This tells us that the consumer surplus is 250.

To find the producer surplus, we find the area of the triangle whose vertices are the equilibrium quantity, the minimum price (y-intercept of the supply curve) and the equilibrium price.

First, we find the y-intercept of the supply curve.  This is the price where the quantity supplied (Q) will be 0.  We do this using the equation for the supply curve.

Q = 5P

0 = 5P

P = 0

This tells us that no labor will be supplied when the price is zero.

We can now find the producer surplus by finding the area of the triangle.  The base of the triangle is found by subtracting the minimum price from the equilibrium.  In this case, that is 10 - 0  = 10.  The height of the triangle is found by finding how far the equilibrium quantity is from the y-axis (50).

Using the formula for the area of a triangle, we have

Producer surplus = ½ (10*50)

= ½ (500)

= 250

So the producer surplus is 250.

To find the total surplus, we simply add the producer surplus and the consumer surplus.

250 + 250 = 500

The total surplus is 500.

To recap, then:

  • equilibrium price is $10
  • equilibrium quantity is 50
  • consumer surplus is 250
  • producer surplus is 250
  • total surplus is 500
justaguide eNotes educator| Certified Educator

The demand curve for labor is  Q=100-5P and the supply curve is Q=5P.

At the equilibrium point, the demand curve and the supply curve intersect each other. If the equilibrium price is Pe, the quantity buyers are willing to buy at Pe is equal to the quantity sellers are willing to sell.

To determine Pe, solve 100 - 5Pe = 5*Pe.

100 = 10*Pe

Pe = 100/10 = 10

The equilibrium price is 10.

At this price on the demand curve, the quantity demanded is equal to 100 - 5*10 = 50. On the supply curve, the quantity supplied is also equal to 50.

Consumer surplus is a way to quantify consumer benefit. It is equal to the difference between the amount that consumers are willing to pay for a service and the amount that they actually pay for it.

The demand curve we are given is Q=100-5P. If the price of labor is 0, the quantity demanded is 100. Consumer surplus is the area below the demand curve for which price is greater than the equilibrium price.

This is equal to (1/2)*(20-10)*(100-50) = 0.5*10*50 = 250

Producer surplus is the amount received by the seller from the market greater than the minimum amount that he is willing to offer his service for.

Here, the supply graph is given by Q = 5P. If the price of labor is equal to 0, the supply drops to 0. The area above the supply curve for which quantity is less than the equilibrium quantity.

This is equal to (1/2)*(10)*50 = 250

The sum of consumer surplus and producer surplus is the total surplus.

Here, total surplus is equal to 250 + 250 = 500

The equilibrium price is equal to 10, equilibrium quantity is equal to 50, consumer surplus is equal to 250, producer surplus is equal to 250, and total surplus is equal to 500.