Suppose that a market is initially in equilibrium. The initial demand curve is $P = 90 - Q ^ { d }$ . The initial supply curve is $P = 2 Q ^ { 5 }$ . Suppose that the government imposes a $3 tax on this market. How much of this $3 is paid for by producers?
A) $0.
B) $1.
C) $1.50.
D) $2.

Question

Quizplus · Accepted Answer

After imposing a tax of $3, the new supply curve becomes $P = 2 Q ^ { 5 } + 3$. In order to find the new equilibrium price, we need to find the quantity demanded and supplied at this new supply curve.

Setting the demand and supply equations equal to each other, we have:

$$90 - Q_d = 2 Q_s^5 + 3$$
$$Q_d = 87 - 2 Q_s^5$$

By substituting the supply equation $P = 2 Q ^ { 5 } + 3$ into the demand equation, we get:

$$90 - (2 Q_s^5 + 3) = 87 - 2 Q_s^5$$
$$Q_s^5 = 1$$

So the new equilibrium quantity is $Q_s = 1$ and the new equilibrium price is:

$$P = 2 (1) ^ 5 + 3 = 5$$

Therefore, the price paid by consumers after the tax is $5 per unit, and the price received by producers is $2 per unit. The amount of tax paid by producers is the difference between these two prices, which is $3 - $2 = $1.

Suppose That a Market Is Initially in Equilibrium P=90−QdP = 90 - Q ^ { d }P=90−Qd

Suppose That a Market Is Initially in Equilibrium $P = 90 - Q ^ { d }$