To calculate how much of the subsidy is received by the producer, we first need to understand how the subsidy impacts the market and then calculate the change in the equilibrium price received by the producer after the subsidy.

Step 1: Simplify the Supply Function

Given the supply function:

$3P_s - 3.29Q_s = 201$

We can rewrite it as:

$P_s = \frac{201 + 3.29Q_s}{3}$

Simplifying:

$P_s = 67 + 1.0967Q_s$

Step 2: Simplify the Demand Function

Given the demand function:

$2P_d + 2.5Q_d = 616$

We can rewrite it as:

$P_d = \frac{616 - 2.5Q_d}{2}$

Simplifying:

$P_d = 308 - 1.25Q_d$

Step 3: Incorporate the Subsidy

When a subsidy of $9 per unit is provided by the government, the price received by producers increases by the amount of the subsidy.

Let $P_s'$ represent the new price received by producers:

$P_s' = P_d + 9$

Substituting the demand equation into this:

$67 + 1.0967Q_s = 308 - 1.25Q_s + 9$

Simplifying:

$1.0967Q_s + 1.25Q_s = 250$

$2.3467Q_s = 250$

$Q_s = \frac{250}{2.3467} \approx 106.53 \text{ units}$

Step 4: Calculate the Price Received by Producers

Substitute $Q_s$ back into the supply equation to find the new price $P_s'$:

$P_s' = 67 + 1.0967 \times 106.53 \approx 67 + 116.79 = 183.79$

Step 5: Determine the Price Before the Subsidy

To find how much of the subsidy is received by the producer, we need to know the price without the subsidy.

Use the original supply function with the new quantity:

$P_s = 67 + 1.0967 \times 106.53 \approx 183.79$

So, the price received by the producer before the subsidy:

$P_s = 67 + 1.0967 \times 106.53 \approx 183.79$

Step 6: Calculate the Producer's Share of the Subsidy

The producer's share of the subsidy is the difference between the new price and the price before the subsidy:

$\text{Producer's share of the subsidy} = P_s' - P_s = 183.79 - 183.79 + 9 = 9$

Since both prices have been calculated to be the same, we conclude the producers do not benefit from the subsidy. Thus, the amount of the subsidy received by the producer is $9 per unit.

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Here are 5 related questions:

1. What would be the effect of the subsidy on consumer surplus?
2. How would the equilibrium quantity change if the subsidy were increased?
3. What would happen to producer surplus if the government removed the subsidy?
4. Can we calculate the deadweight loss due to the subsidy?
5. How does the incidence of the subsidy compare between producers and consumers?

Tip: When dealing with subsidies, it’s important to analyze both the pre-subsidy and post-subsidy market conditions to accurately determine the distribution of the subsidy between consumers and producers.