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.