Question 1183246: Let P = 0.09q + 50 be the supply equation for a manufacturer. The demand equation for his product is:
P = 0.07q + 65
If a tax of N1.50/unit is to be imposed on the manufacturer, how will the original equilibrium price be effected if the demand remains the same?
Determine the total revenue obtained by the manufacturer at the equilibrium point, both before and after the tax.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Here's how to analyze the impact of the tax on the equilibrium price and revenue:
**1. Find the original equilibrium:**
* Set the supply and demand equations equal to each other:
0.09q + 50 = 0.07q + 65
* Solve for q (equilibrium quantity):
0.02q = 15
q = 750
* Substitute the value of q back into either the supply or demand equation to find P (equilibrium price):
P = 0.09(750) + 50
P = 117.5
**2. Incorporate the tax:**
A tax of N1.50/unit increases the supply equation by that amount. The new supply equation is:
P_taxed = 0.09q + 50 + 1.50
P_taxed = 0.09q + 51.5
**3. Find the new equilibrium (after tax):**
* Set the new supply equation equal to the original demand equation:
0.09q + 51.5 = 0.07q + 65
* Solve for the new equilibrium quantity (q_taxed):
0.02q = 13.5
q_taxed = 675
* Substitute q_taxed back into the *original* demand equation to find the price the *consumer* pays (P_consumer):
P_consumer = 0.07(675) + 65
P_consumer = 112.25
* The manufacturer receives the consumer price *minus* the tax:
P_manufacturer = P_consumer - 1.50
P_manufacturer= 112.25 - 1.50 = 110.75
**4. Analyze the price effect:**
The equilibrium price *paid by the consumer* increased from N117.5 to N112.25. However, the price *received by the manufacturer* decreased from N117.50 to N110.75.
**5. Calculate total revenue:**
* **Before tax:**
Revenue_before = P * q = 117.5 * 750 = N88,125
* **After tax:**
Revenue_after = P_manufacturer * q_taxed = 110.75 * 675 = N74,756.25
**Summary:**
* The tax caused the equilibrium quantity to decrease from 750 to 675.
* The price paid by the consumer decreased from N117.50 to N112.25.
* The price received by the manufacturer decreased from N117.50 to N110.75.
* The total revenue decreased from N88,125 to N74,756.25.
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