The long-run supply curve for a good is a horizontal line at a price $3 per unit of the good. The demand curve for the good is QD = 50-2P.

(a) What is the equilibrium output of the good?
(b) A $1 excise tax is imposed on the good. What will be the long-run effect on the equilibrium output of the good? Explain.
(c) Shortly after the tax is imposed, a unit of the good can be purchased for $3.60. Is this the long-run equilibrium price? Explain.

(a) To find the equilibrium output of the good, we need to set the quantity demanded (QD) equal to the quantity supplied (QS).

Given:
QD = 50 - 2P
QS is a horizontal line at $3 per unit

Setting QD equal to QS:
50 - 2P = QS = QD = 3

Now, let's solve for P to find the equilibrium price:
50 - 2P = 3
-2P = 3 - 50
-2P = -47
P = -47 / -2
P = $23.50

To find the equilibrium output, we substitute the equilibrium price (P) back into the demand function:
QD = 50 - 2P
QD = 50 - 2(23.50)
QD = 50 - 47
QD = 3

Therefore, the equilibrium output of the good is 3 units.

(b) When a $1 excise tax is imposed on the good, the equilibrium output will be affected in the long run. An excise tax- also called a per-unit sales tax- increases the cost of production and reduces the amount of quantity supplied.

In this case, since the long-run supply curve is a horizontal line at $3 per unit, the imposition of a $1 excise tax will increase the cost of production to $4 per unit ($3 + $1).

As a result, the quantity supplied (QS) will decrease, as producers are less willing to supply the good at a higher cost. The new equilibrium quantity will be lower than before the tax.

(c) A unit of the good being purchased for $3.60 is not the long-run equilibrium price. In the long run, the equilibrium price is determined by the intersection of the demand curve (QD) and the long-run supply curve (QS).

In this scenario, the long-run supply curve is a horizontal line at $3 per unit. So, the long-run equilibrium price will be $3.

If a unit of the good is being purchased for $3.60, it implies that the market price is higher than the long-run equilibrium price. This could be due to factors like temporary changes in supply or demand, imbalances in the market, or the impact of the excise tax. Over time, the market will adjust, and the price will move towards the long-run equilibrium price of $3.