Agricultural Economics- ICAR JRF/SRF 2024

• Amortized Decreasing Repayment Plan:
• In an amortized decreasing repayment schedule (also known as the equal principal installment plan):
• Principal Payment Remains Constant: In every period, the farmer repays a fixed, equal fraction of the principal ($P = \frac{\text{Total Principal}}{N}$).
• Interest Decreases: Interest is charged strictly on the remaining outstanding loan balance. As principal is repaid each year, the outstanding debt declines, causing the interest payment to decrease systematically.
• Total Installment Decreases: Since total installment = Constant Principal + Decreasing Interest, the overall installment decreases over time.
• Conclusion: Installment and interest decrease, while principal repayment remains constant, corresponding to Option 4.

Correct option: (4) Installment and interest decreases, principal remains same

• Cobb-Douglas Production Function Elasticity of Substitution:
• Assertion (A) is true: A standard Cobb-Douglas production function ($Y = A X_1^{\alpha} X_2^{\beta}$) has an elasticity of substitution ($\sigma$) identically equal to 1.
• Reason (R) is true and is the correct explanation of (A): The elasticity of substitution measures the percentage change in factor proportions relative to the percentage change in the marginal rate of technical substitution ($MRTS$):

Along any specific isoquant of a Cobb-Douglas surface, a $1\%$ change in the factor ratio $\frac{X_2}{X_1}$ results in an exact $1\%$ proportional change in $MRTS$, making $\sigma = 1$ everywhere along the isoquant.

• Conclusion: Both (A) and (R) are true, and (R) is the correct explanation of (A), making Option 1 correct.

Correct option: (1) Both (A) and (R) are true and (R) is the correct explanation of (A)

• Isoquant Geometry: Ridge Lines, Expansion Path, and Isoclines:
• Ridge Lines $\rightarrow RTS = -\frac{dX_1}{dX_2} = 0$ (and $\infty$): Ridge lines delineate the economic region of production. Along the upper ridge line, $MP_2 = 0$ ($RTS = 0$); along the lower ridge line, $MP_1 = 0$ ($RTS = \infty$).
• Expansion Path $\rightarrow RTS_{ij} = -\frac{dX_i}{dX_j} = -\frac{P_i}{P_j}$: The expansion path is the locus of least-cost factor combinations where the slope of the isoquant ($RTS$) equals the inverse factor price ratio.
• Isocline $\rightarrow RTS_{ij} = -\frac{dX_i}{dX_j} = c$: An isocline is any line or curve passing through points on different isoquants where the rate of technical substitution is constant ($c$).
• Correct Sequence: (C), (B), (A), corresponding to Option 1.

Correct option: (1) (C), (B), (A).