The demand and supply functions for a product are given as:
Pd =439 - 4Qd
Ps = 87+5Qs
where Q represents the quantity (in units) and P is the price (in $/unit). The government imposes a tax of $6.3 per unit sold. Calculate how much of the tax burden is borne by the consumer (in $/unit).
Note: Round your answer to 2-decimal places.

To determine how much of the tax burden is borne by the consumer, we need to calculate the new equilibrium price and quantity after the tax is imposed. The tax affects the supply curve because it increases the cost per unit for suppliers. Here's the step-by-step process:

### Step 1: Find the initial equilibrium without tax
The initial equilibrium occurs when the quantity demanded equals the quantity supplied ($Q_d = Q_s = Q$).

Given:
- Demand function: $P_d = 439 - 4Q$
- Supply function: $P_s = 87 + 5Q$

At equilibrium:
\[
P_d = P_s
\]

So, equating the demand and supply functions:
\[
439 - 4Q = 87 + 5Q
\]

Now, solve for $Q$. 

### Step 2: Find the new supply function with tax
The tax of $6.3 per unit increases the price suppliers effectively receive. Thus, the new supply function shifts up by the amount of the tax:

\[
P_s' = P_s + 6.3 = 87 + 5Q + 6.3 = 93.3 + 5Q
\]

### Step 3: Find the new equilibrium with the tax
Now, set the new supply function equal to the demand function to find the new equilibrium quantity:

\[
439 - 4Q = 93.3 + 5Q
\]

Solve this equation for the new equilibrium quantity, $Q_{new}$.

### Step 4: Calculate the new equilibrium prices
Substitute $Q_{new}$ into the demand and the new supply function to find the prices paid by consumers and received by suppliers:
- Price paid by consumers: $P_{consumer} = 439 - 4Q_{new}$
- Price received by suppliers: $P_{supplier} = 93.3 + 5Q_{new}$

### Step 5: Determine the tax burden on the consumer
The tax burden on the consumer is the difference between the new price paid by consumers and the initial equilibrium price.

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

- **Initial equilibrium quantity ($Q_{initial}$)**: approximately 39.11 units
- **Initial equilibrium price ($P_{initial}$)**: approximately $282.56 per unit
- **New equilibrium quantity ($Q_{new}$)**: approximately 38.41 units
- **Price paid by consumers after tax ($P_{consumer}$)**: approximately $285.36 per unit
- **Price received by suppliers after tax ($P_{supplier}$)**: approximately $285.36 per unit

**Tax burden borne by the consumer**: $2.80 per unit.

Would you like further details or have any questions? 

Here are some related questions:
1. How do you calculate the equilibrium quantity and price without a tax?
2. How does the tax affect the supply and demand equilibrium?
3. What is the economic significance of the tax burden distribution between consumers and producers?
4. How would the results change if the tax were imposed on consumers instead of producers?
5. What impact does elasticity have on tax incidence?

**Tip:** The more inelastic the demand, the larger the tax burden on consumers.

Understand how to calculate the tax burden on consumers and suppliers using supply and demand analysis. Explore the impact of a $6.3 per unit tax on equilibrium quantity and price. Detailed step-by-step solution provided.

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