Math Problem Statement

just give me a direct answer for the 3 questions and use the graph to help answer them

After the subsidy, what is the amount of consumer surplus, producer surplus, and government spending? Use the graph provided to help calculate these values.

Solution

To answer your questions, I'll use the graph in the first image and break down the needed calculations from the second image.

Here’s how we can solve the three questions based on the provided graph:

1. Consumer Surplus After Subsidy

Consumer surplus is the area of the triangle between the demand curve and the price consumers pay. From the graph:

  • The equilibrium price after the subsidy is at $4.
  • The highest price on the demand curve (where quantity is 0) is $10.

The consumer surplus is the area of the triangle formed by:

  • The height is 104=610 - 4 = 6 (from the top of the demand curve to the price after subsidy).
  • The base of the triangle is the quantity at the subsidy equilibrium, which is 60.

Thus, the consumer surplus formula for the area of a triangle is:

Consumer Surplus=12×base×height=12×60×6=180\text{Consumer Surplus} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 60 \times 6 = 180

So, Consumer Surplus = $180.


2. Producer Surplus After Subsidy

Producer surplus is the area of the triangle between the supply curve and the price producers receive. After the subsidy:

  • Producers receive $6 per unit.
  • The lowest price on the supply curve (where quantity is 0) is $1.

The producer surplus is the area of the triangle formed by:

  • The height is 61=56 - 1 = 5.
  • The base is the quantity at the subsidy equilibrium, which is 60.

Thus, the producer surplus is:

Producer Surplus=12×base×height=12×60×5=150\text{Producer Surplus} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 60 \times 5 = 150

So, Producer Surplus = $150.


3. Government Spending on the Subsidy

The government spending is calculated by:

  • The subsidy per unit, which is 64=26 - 4 = 2 dollars (the difference between the price producers receive and the price consumers pay).
  • The quantity sold after the subsidy, which is 60 units.

Thus, government spending is:

Government Spending=Subsidy per unit×Quantity=2×60=120\text{Government Spending} = \text{Subsidy per unit} \times \text{Quantity} = 2 \times 60 = 120

So, Government Spending = $120.


Summary:

  1. Consumer Surplus = $180
  2. Producer Surplus = $150
  3. Government Spending = $120

Would you like a more detailed explanation of any part, or do you have any questions?

Here are 5 related questions for deeper understanding:

  1. How would consumer surplus change if the subsidy increased?
  2. Can you explain how the subsidy affects both consumer and producer surplus?
  3. What would the graph look like without any subsidy?
  4. How do subsidies influence the market equilibrium price and quantity?
  5. How does government spending on subsidies impact overall welfare in this market?

Tip: Remember, a subsidy shifts the supply curve down (to the right), lowering prices for consumers and increasing producer surplus.

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Math Problem Analysis

Mathematical Concepts

Supply and Demand Curves
Consumer Surplus
Producer Surplus
Subsidies

Formulas

Consumer Surplus = (1/2) * base * height
Producer Surplus = (1/2) * base * height
Government Spending = Subsidy per unit * Quantity

Theorems

Basic economic theory on subsidies
Surplus calculation

Suitable Grade Level

Undergraduate Economics