Suppose that a market is initially in equilibrium. The initial demand curve is $P = 90 - Q ^ { d }$. The initial supply curve is $P = 2 Q ^ { s }$. Suppose that the government imposes a $\$ 3$ tax on this market. What are the government receipts from the tax?
A)$90.
B)$87.
C)$45.
D)$43.50.

Question

Quizplus · Accepted Answer

The initial equilibrium is found where the demand curve equals the supply curve: $90 - Q^d = 2Q^s$. Since $Q^d = Q^s = Q$, we can solve for $Q$ to find the equilibrium quantity. This gives us $90 - Q = 2Q$, leading to $3Q = 90$, so $Q = 30$. The tax shifts the supply curve up by $3, making the new supply equation $P = 2Q + 3$. Setting the new supply equal to the original demand, $90 - Q = 2Q + 3$, we find the new equilibrium quantity, $Q = 29$. The government receipts from the tax are the tax amount ($3) times the new quantity sold (29), which equals $87.

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 $P = 90 - Q ^ { d }$