The demand and supply functions for a product are given as:

2Pa + 2.6Qd = 626

3Ps - 3.5Qs = 210

where Q represents the quantity (in units) and P is the price (in $/unit). The government provides a subsidy of $16 per unit sold. Calculate how much of the subsidy is received by the producer (in $/unit).

Note: Round your answer to 2-decimal places.

To determine how much of the subsidy is received by the producer, we need to calculate the new equilibrium price and quantity after the subsidy is provided. A subsidy effectively lowers the cost per unit for producers, shifting the supply curve down by the amount of the subsidy.

### Step-by-Step Solution:

### Step 1: Find the initial equilibrium without subsidy
Given the equations:
- Demand function: $ 2P_d + 2.6Q_d = 626 $
- Supply function: $ 3P_s - 3.5Q_s = 210 $

At equilibrium, $ Q_d = Q_s = Q $ and $ P_d = P_s = P $. We solve these equations simultaneously to find the initial equilibrium price and quantity.

### Step 2: Find the new supply function with the subsidy
The subsidy of $16 per unit decreases the effective price for producers, so the new supply function becomes:
\[
3P_s' - 3.5Q = 210 - 16
\]

Simplify this to get the new supply equation.

### Step 3: Find the new equilibrium with the subsidy
Set the demand function equal to the new supply function to find the new equilibrium quantity, $ Q_{new} $.

### Step 4: Calculate the new equilibrium prices
Substitute $ Q_{new} $ into the demand and new supply function to find the prices paid by consumers and received by suppliers:
- Price received by suppliers: $ P_{producer} $
- Price paid by consumers: $ P_{consumer} $

### Step 5: Determine the subsidy received by the producer
The subsidy received by the producer is the difference between the new price received by the producer and the initial equilibrium price.

Let's perform the calculations to determine these values.The calculations yield the following results:

- **Initial equilibrium price ($P_{initial}$)**: approximately $184.93 per unit
- **Initial equilibrium quantity ($Q_{initial}$)**: approximately 98.51 units
- **New equilibrium price ($P_{new}$)**: approximately $182.12 per unit
- **New equilibrium quantity ($Q_{new}$)**: approximately 100.68 units
- **Subsidy received by the producer**: $-$2.80$ per unit

The negative value indicates that the producer effectively benefits less in price due to market adjustments, receiving $2.80 less per unit than before.

Would you like further clarification or have any questions?

Here are some related questions:
1. How does a subsidy generally affect supply and demand curves?
2. Why does the price received by producers decrease even with a subsidy?
3. How is the distribution of subsidy benefits between producers and consumers determined?
4. What factors could influence the effectiveness of a subsidy policy?
5. How would the market react if the subsidy were increased or decreased?

**Tip:** Subsidies can lead to unexpected market behaviors; understanding the elasticity of demand and supply is crucial to predict these effects.

Explore how subsidies affect producers' income using demand and supply equations. Calculate the subsidy received per unit with step-by-step analysis. Understand market equilibrium adjustments and economic impacts.

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