Quantitative Analysis of Consumer and Producer Surplus at Equilibrium: Videos & Practice Problems

To calculate consumer and producer surplus, first determine the equilibrium price and quantity where quantity demanded equals quantity supplied. Use the demand and supply equations to find the axis prices when quantity demanded and supplied equal zero. Consumer surplus is the area above the equilibrium price and below the demand curve, while producer surplus is the area below the equilibrium price and above the supply curve. The formulas for these areas involve calculating the base and height of the respective triangles formed on the graph.

Quantitative Analysis of Consumer and Producer Surplus

To calculate consumer and producer surplus, we first need to determine the equilibrium price and quantity in a market. This involves setting the quantity demanded equal to the quantity supplied and solving for the price. For example, if we have the demand equation Qd = 3,000,000 - 1,000P and the supply equation Qs = 1,300P - 450,000, we can find the equilibrium by equating these two equations:

3,000,000 - 1,000P = 1,300P - 450,000

By rearranging the equation to isolate P, we can solve for the equilibrium price P*. After performing the necessary algebra, we find that P* = 1,500. To find the equilibrium quantity Q*, we substitute P* back into either the demand or supply equation, yielding Q* = 1,500,000.

Next, we need to determine the axis prices, which are the prices at which the quantity demanded or supplied equals zero. For the demand axis price, we set Qd = 0:

0 = 3,000,000 - 1,000P

Solving this gives us the demand axis price of P = 3,000. Similarly, for the supply axis price, we set Qs = 0:

0 = 1,300P - 450,000

This results in a supply axis price of approximately P = 346.15, which we can round to P = 346.

With these values, we can now calculate consumer and producer surplus. Consumer surplus is the area above the equilibrium price and below the demand curve. It can be calculated using the formula for the area of a triangle:

Consumer Surplus = 0.5 × Base × Height

Here, the base is the difference between the demand axis price and the equilibrium price (3,000 - 1,500 = 1,500), and the height is the equilibrium quantity (Q* = 1,500,000). Thus:

Consumer Surplus = 0.5 × 1,500 × 1,500,000 = 1,125,000,000

For producer surplus, we look at the area below the equilibrium price and above the supply curve. Using the same triangle area formula, the base is the difference between the equilibrium price and the supply axis price (1,500 - 346 = 1,154), and the height remains the equilibrium quantity:

Producer Surplus = 0.5 × Base × Height

Thus:

Producer Surplus = 0.5 × 1,154 × 1,500,000 = 865,500,000

In summary, the consumer surplus is 1,125,000,000 and the producer surplus is 865,500,000. These calculations illustrate how to derive consumer and producer surplus using equilibrium analysis and basic algebraic principles.

The supply and demand curves for a product are as follows. What is consumer surplus in this market? 
Q_D = 45 – 2P 
Q_S = -15 + P

• A. 6.25
• B. 12.5
• C. 20
• D. 22.5
• E. 25

Answer: (A)

The supply and demand curves for a product are as follows. What is producer surplus in this market? 
Q_D = 45 – 2P 
Q_S = -15 + P

• A. 6.25
• B. 12.5
• C. 15
• D. 20
• E. 25

Answer: (B)

Here’s what students ask on this topic:

How do you calculate consumer and producer surplus at equilibrium?

To calculate consumer and producer surplus at equilibrium, first determine the equilibrium price (P*) and quantity (Q*) where quantity demanded equals quantity supplied. Use the demand and supply equations to find the axis prices when quantity demanded and supplied equal zero. Consumer surplus is the area above the equilibrium price and below the demand curve, while producer surplus is the area below the equilibrium price and above the supply curve. The formulas for these areas involve calculating the base and height of the respective triangles formed on the graph.

What is the formula for consumer surplus?

The formula for consumer surplus is given by the area of the triangle above the equilibrium price and below the demand curve. Mathematically, it is:

$\frac{1}{2}\times (P_d-P_{*})\times Q_{*}$

where Pd is the demand axis price, P* is the equilibrium price, and Q* is the equilibrium quantity.

What is the formula for producer surplus?

The formula for producer surplus is given by the area of the triangle below the equilibrium price and above the supply curve. Mathematically, it is:

$\frac{1}{2}\times (P_{*}-P_s)\times Q_{*}$

where P* is the equilibrium price, Ps is the supply axis price, and Q* is the equilibrium quantity.

How do you find the equilibrium price and quantity?

To find the equilibrium price and quantity, set the quantity demanded equal to the quantity supplied. This involves solving the demand and supply equations simultaneously. For example, if the demand equation is $Q$_d = 3000 - 1000P and the supply equation is $Q$_s = 1300P - 450, set $Q$_d = Q_s and solve for P. Once P (equilibrium price) is found, substitute it back into either equation to find Q (equilibrium quantity).

What are axis prices in the context of consumer and producer surplus?

Axis prices refer to the prices at which the quantity demanded or supplied equals zero. The demand axis price is where the demand curve intersects the price axis, and the supply axis price is where the supply curve intersects the price axis. These prices are used to calculate the base of the triangles representing consumer and producer surplus. For example, if the demand equation is $Q$_d = 3000 - 1000P, setting $Q$_d = 0 and solving for P gives the demand axis price.