Question

A consumer spends his entire income on goods \(X\) and \(Y\). The price of \(X\) is \(₹20\) per unit and the price of \(Y\) is \(₹10\) per unit. If his income is \(₹400\), which of the following combinations lies on his budget line?

• A. \(X=5,\;Y=25\)
• B. \(X=10,\;Y=20\)
• C. \(X=15,\;Y=5\)
• D. \(X=8,\;Y=18\)

Hint:

To quickly identify a point on a budget line, substitute the values directly into: \[ P_X X + P_Y Y=M \] If LHS = RHS, the point lies on the budget line.

Answer 1

The Correct Option is B

Concept: A budget line represents all possible combinations of two goods that can be purchased with a given income at given prices. The budget equation is: \[ P_X X + P_Y Y=M \] where:
• \(P_X\) = Price of Good \(X\)
• \(P_Y\) = Price of Good \(Y\)
• \(M\) = Income Any combination satisfying the equation lies exactly on the budget line.

Step 1: Write the budget equation. Given: \[ P_X=20 \] \[ P_Y=10 \] \[ M=400 \] Therefore, \[ 20X+10Y=400 \] Dividing by \(10\), \[ 2X+Y=40 \]

Step 2: Check Option A. \[ 2(5)+25=35 \] \[ 35\neq40 \] Hence, not on the budget line.

Step 3: Check Option B. \[ 2(10)+20=40 \] \[ 40=40 \] Hence, this combination lies exactly on the budget line.

Step 4: Verify remaining options. Option C: \[ 2(15)+5=35 \] Not equal to \(40\). Option D: \[ 2(8)+18=34 \] Not equal to \(40\). Only Option B satisfies the budget equation. Therefore, \[ \boxed{X=10,\;Y=20} \] lies on the budget line.