The problem gives the demand function $75p + q = 2400$ and the supply function $150p - q = 675$. A tax of $0.50 per item is levied. We need to find the equilibrium price and quantity after the tax is levied.

1. Problem Description

The problem gives the demand function $75p + q = 2400$ and the supply function $150p - q = 675$. A tax of $0.50 per item is levied. We need to find the equilibrium price and quantity after the tax is levied.

2. Solution Steps

First, we need to consider the effect of the tax on the supply function. Since the tax is levied on the supplier, it effectively increases the price the supplier needs to receive for each unit. Thus, the new price the supplier receives is $p - 0.50$. The original supply function is $150p - q = 675$. Substituting $p-0.50$ for $p$, we have:

$150(p - 0.50) - q = 675$

$150p - 75 - q = 675$

$150p - q = 675 + 75$

$150p - q = 750$

This is the new supply function.

The demand function remains the same: $75p + q = 2400$.

Now we need to solve the system of equations:

$150p - q = 750$

$75p + q = 2400$

Adding the two equations, we get:

$150p - q + 75p + q = 750 + 2400$

$225p = 3150$

$p = \frac{3150}{225}$

$p = 14$

Now, we substitute the value of $p$ into the demand function $75p + q = 2400$:

$75(14) + q = 2400$

$1050 + q = 2400$

$q = 2400 - 1050$

$q = 1350$

3. Final Answer

The equilibrium price is $14 and the equilibrium quantity is$

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