The following diagram shows a farmer’s choice between free time and grain before (A) and after (B) an improvement in technology. Based on this information, read the following statements and select the correct one(s).

Question

BlackTom AI · Accepted Answer

At the optimum MRS (marginal rate of substitution) equals MRT (marginal rate of transformation), so the farmer’s chosen point on a feasible frontier is where his private trade-off between free time and grain equals the technology-imposed trade-off.

1) Relevant knowledge points and concepts
- Feasible frontier (production possibility/frontier) shows the trade-off between free time and grain; its slope (in absolute value) is the MRT, the opportunity cost of one more unit of free time measured in forgone grain.
- An indifference curve represents preferences; its slope is the MRS, the rate at which the farmer is willing to trade grain for free time.
- The optimal choice on a frontier is the tangency where MRS = MRT (or a corner if tangency is not feasible).
- A technological improvement shifts the feasible frontier outward (expands choices) but does not by itself determine which direction along the new frontier the farmer will move.

2) Step-by-step reasoning
- Before the improvement the farmer chooses A where MRS_A = MRT_A.
- Technology shifts the frontier outward to a new locus; B is a point on that new frontier (perhaps the tangency if drawn that way).
- The farmer’s new optimum must satisfy MRS_new = MRT_new at some point on the new frontier. Whether that tangency lies to the left of B (more grain, less free time), at B, or to the right of B (more free time) depends on the shape of preferences (indifference curves) and the exact change in MRT across the frontier.
- Therefore the farmer may end up with more free time than at B or less — both are possible outcomes.

3) Intermediate steps / expressions
- Optimality condition: MRS(free time for grain) = MRT(free time → grain).
- Change in technology alters MRT(x) as a function of free time x; the sign of Δx (movement relative to B) depends on solving MRS_new(x) = MRT_new(x).

4) Why the correct answer is correct
- The statement “The farmer may choose a point on either side of B after the technology improvement” is correct because the final chosen point depends on preferences (MRS) relative to the new MRT profile; an outward shift alone does not uniquely determine movement direction.

5) Why other options are incorrect
- Option 1: Comparing MRTs at A and B and claiming this “gives the farmer an incentive to take more free time” is incorrect because an incentive requires comparing MRS to MRT at the optimum, not just MRT levels.
- Option 2: Saying a larger MRS at B necessarily gives an incentive for more free time is wrong; only the equality/relative position of MRS and MRT determines direction.
- Option 3: Claiming the farmer will definitely choose a point to the right of B is too strong; preferences could lead to a choice left of B.

6) Conclusion
The correct choice is that the farmer may choose a point on either side of B after the technology improvement, which matches the provided answer.

The following diagram shows a farmer’s choice between free time and grain before (A) and after (B) an improvement in technology. Based on this information, read the following statements and select the correct one(s). 多项选择题

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