The inverse demand function for eggs is p = 125

Question

The inverse demand function for eggs is p = 125 - 6q, where q is the number of cases of eggs. The inverse supply is p = 5 + 6q. In the past, eggs were not taxed, but now a tax of 72 dollars per case has been introduced. What is the effect of the tax on the quantity of eggs supplied?

Quizplus · Accepted Answer

Before the tax, at the equilibrium point, the quantity demanded (Qd) equals the quantity supplied (Qs). So, we have:

125 - 6Q = 5 + 6Q
12Q = 120
Q = 10

The equilibrium price (Pe) can be found by substituting the value of Q into either the demand or supply equation. Let's use the demand equation:

Pe = 125 - 6Q
Pe = 125 - 6(10)
Pe = 65

So, before the tax, the equilibrium price is 65 dollars per case, and the quantity exchanged is 10 cases.

Now, with the tax of 72 dollars per case, the new supply function becomes:

p = 5 + 6q - 72
p = -67 + 6q

We need to find the new equilibrium quantity (Qs') by equating Qd and Qs':

125 - 6Qd' = -67 + 6Qs'
192 = 12Qs'
Qs' = 16

So, with the tax, the quantity supplied drops from 10 cases to 16 cases, a decrease of 6 cases. Therefore, the correct answer is C.