Question

There are two regions in a country. The demand for chocolates in region 1 is given by
\[ Q_1(P) = 100 - P \] and the demand for chocolates in region 2 is given by
\[ Q_2(P) = 200 - P \] where \( Q_1(P) \) and \( Q_2(P) \) denote the demand for chocolates in region 1 and 2 respectively at a price \( P \). There is only one seller who is licensed to sell chocolates in the country. Suppose the seller sets a price of \( P = 125 \). The total demand for chocolates in the country at this price is

• A. 50
• B. 75
• C. 100
• D. 125

Hint:

When calculating total demand, remember to add the demands from each region and account for any regions with zero demand.

Answer 1

The Correct Option is B

Step 1: Analyzing the demand equations.
The demand in region 1 is given by \( Q_1(P) = 100 - P \), and in region 2 by \( Q_2(P) = 200 - P \). These equations tell us the quantity demanded at a given price. Step 2: Substituting the price \( P = 125 \) into the demand equations.
For region 1: \[ Q_1(125) = 100 - 125 = -25 \quad (\text{but demand cannot be negative, so demand is 0 in region 1}). \] For region 2: \[ Q_2(125) = 200 - 125 = 75. \] Step 3: Total demand in the country.
The total demand for chocolates in the country is the sum of the demands in the two regions: \[ \text{Total demand} = Q_1(125) + Q_2(125) = 0 + 75 = 75. \] Step 4: Conclusion.
The total demand for chocolates at a price of \( P = 125 \) is 75, so the correct answer is (B).