Question

If by increasing the quantity of input $X_1$ by one unit, the farmer can give up two units of input $X_2$ and still produce the same output, then the $MRS_{X1,X2}$ is:

• A. 0.5
• B. 0
• C. 0
• D. 0

Hint:

The subscript order $MRS_{A, B}$ represents the amount of input B we are willing to substitute/give up per unit of input A gained. Thus, it is simply $\text{units of B given up} / \text{units of A added}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The Marginal Rate of Substitution (MRS) or Marginal Rate of Technical Substitution (MRTS) of input $X_1$ for input $X_2$ measures the rate at which one input can be substituted for another while keeping the level of total output constant.

Step 2: Key Formula or Approach:
The formula for the Marginal Rate of Substitution of input $X_1$ for input $X_2$ is: \[ MRS_{X1,X2} = -\frac{\Delta X_2}{\Delta X_1} \]

Step 3: Detailed Explanation:
From the problem statement, we are given:
- The change in the quantity of input $X_1$ ($\Delta X_1$) is $+1$ unit.
- The change in the quantity of input $X_2$ ($\Delta X_2$) is $-2$ units (since the farmer gives up two units of $X_2$).
Now, let us substitute these values into the MRS formula: \[ MRS_{X1,X2} = -\frac{-2}{1} = 0 \]
This means that 1 unit of input $X_1$ is equivalent to 2 units of input $X_2$ in terms of productive capacity at this point on the isoquant.

Step 4: Final Answer:
The value of $MRS_{X1,X2}$ is 0.