Question

Consider the following demand and supply functions:

• A. The choke price is equal to the market clearing price.
• B. If a \(25\%\) ad valorem tax is imposed by the government, then the new market clearing price is equal to the choke price.
• C. If a \(100\%\) ad valorem tax is imposed by the government, then the choke price still exists.
• D. If a flat-rate tax of Rupees \(10\) per unit is imposed by the government, then the new market clearing price is equal to the choke price.

Hint:

Choke price is found from the demand curve by setting quantity demanded equal to zero. Taxes may change equilibrium price, but they do not remove the choke price implied by the demand function.

Answer 1

The Correct Option is C

Step 1: Find the choke price.
Choke price is the price at which quantity demanded becomes zero.
\[ D(p)=400-8p \] Put
\[ D(p)=0 \] \[ 400-8p=0 \] \[ p=50 \]

Step 2: Find the market clearing price without tax.
Market equilibrium occurs when
\[ D(p)=S(p) \] \[ 400-8p=2p \] \[ 400=10p \] \[ p=40 \]
So, market clearing price is \(40\), not \(50\). Hence, option (A) is incorrect.

Step 3: Check \(25\%\) ad valorem tax.
With a \(25\%\) ad valorem tax, consumer price becomes higher than producer price.
The new equilibrium price will change, but it will not become equal to the choke price \(50\).
Hence, option (B) is incorrect.

Step 4: Check \(100\%\) ad valorem tax.
A \(100\%\) ad valorem tax changes the equilibrium price, but the choke price is determined from the demand curve.
Since the demand function remains
\[ D(p)=400-8p \] the choke price still exists and remains
\[ p=50 \]
Therefore, option (C) is correct.

Step 5: Check flat-rate tax of Rupees \(10\).
With a flat tax of \(10\), if \(p\) is consumer price, producer receives \(p-10\).
Supply becomes
\[ S=2(p-10) \]
Equilibrium condition is
\[ 400-8p=2(p-10) \] \[ 400-8p=2p-20 \] \[ 420=10p \] \[ p=42 \]
So, new market clearing price is not equal to choke price \(50\). Hence, option (D) is incorrect.

Step 6: Final conclusion.
Only statement (C) is correct.
\[ \boxed{(C)} \]