Math Problem Statement
just give me a direct answer for the 3 questions and use the graph to help answer them
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 (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:
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 .
- The base is the quantity at the subsidy equilibrium, which is 60.
Thus, the producer surplus is:
So, Producer Surplus = $150.
3. Government Spending on the Subsidy
The government spending is calculated by:
- The subsidy per unit, which is 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:
So, Government Spending = $120.
Summary:
- Consumer Surplus = $180
- Producer Surplus = $150
- 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:
- How would consumer surplus change if the subsidy increased?
- Can you explain how the subsidy affects both consumer and producer surplus?
- What would the graph look like without any subsidy?
- How do subsidies influence the market equilibrium price and quantity?
- 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
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