In this analysis, we will explore the calculation of key economic concepts such as consumer surplus, producer surplus, and deadweight loss, particularly in the context of price ceilings and floors. Understanding these concepts is crucial for evaluating market efficiency and the impact of government interventions.

To begin, we need to determine the quantity supplied at a given price ceiling. For instance, if the price ceiling is set at $1,000, we can use the supply equation to find the quantity supplied. The equation can be expressed as:

Quantity Supplied = 1300 × Price - 450,000

Substituting the price ceiling into the equation:

Quantity Supplied = 1300 × 1000 - 450,000 = 850,000

This quantity represents the lower quantity supplied due to the price ceiling. It is essential to remember that when dealing with price ceilings, we utilize the supply equation to find the quantity supplied, while for price floors, we would use the demand equation.

Next, we need to find the missing price at this quantity. For a price ceiling, we will use the demand equation:

Quantity Demanded = 3,000,000 - 1,000P

Setting the quantity demanded equal to the quantity supplied (850,000), we rearrange the equation:

1,000P = 3,000,000 - 850,000

Solving for P gives us:

P = (2,150,000) / 1,000 = 2,150

Now that we have both the quantity and the price, we can calculate the producer surplus. Producer surplus is the area below the price level and above the supply curve, typically represented as a triangle. The formula for the area of a triangle is:

Area = 0.5 × Base × Height

In this case, the base is the difference between the price ($1,000) and the minimum price at which producers are willing to sell ($346), and the height is the quantity supplied (850,000):

Producer Surplus = 0.5 × (1,000 - 346) × 850,000 = 277,950,000

Next, we calculate consumer surplus, which is the area above the price level and below the demand curve. This area can be divided into a rectangle and a triangle. The rectangle's area is calculated as:

Rectangle Area = Base × Height

Where the base is the difference between the maximum price consumers are willing to pay ($2,150) and the price level ($1,000), and the height is the quantity (850,000):

Rectangle Area = (2,150 - 1,000) × 850,000 = 977,500,000

For the triangle, we calculate:

Triangle Area = 0.5 × Base × Height

Where the base is the difference between the maximum price ($3,000) and the price consumers pay ($2,150), and the height is the quantity (850,000):

Triangle Area = 0.5 × (3,000 - 2,150) × 850,000 = 361,250,000

Adding both areas together gives us the total consumer surplus:

Total Consumer Surplus = Rectangle Area + Triangle Area = 977,500,000 + 361,250,000 = 1,338,750,000

Finally, we calculate the deadweight loss, which represents the loss of economic efficiency when the equilibrium quantity is not achieved. This area is also a triangle, calculated using the formula:

Deadweight Loss = 0.5 × Base × Height

Where the base is the difference between the prices ($2,150 - $1,000) and the height is the difference between the quantities (1,500,000 - 850,000):

Deadweight Loss = 0.5 × (2,150 - 1,000) × (1,500,000 - 850,000) = 373,750,000

In summary, we have calculated the producer surplus as 277,950,000, the consumer surplus as 1,338,750,000, and the deadweight loss as 373,750,000. These calculations illustrate the effects of price ceilings on market dynamics and the resulting economic inefficiencies.