Given provisions of specific factors model of international trade, explain – examining the economy PPF – what the shape of labor allocation curve should be. Select one – the most appropriate answer.

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Question restatement: The prompt asks, within the framework of the specific factors model of international trade, when we examine the economy’s production possibility frontier (PPF) and the allocation of labor between sectors, what is the expected shape of the labor allocation curve? Answer choices are: 1) Straight line having constant slope. 2) Straight line having varying shape. 3) Increasing curve of a hyperbolic type and flipped around. 4) Decreasing curve of a hyperbolic type and flipped around.

Option 1 analysis: A straight line with constant slope implies a linear trade-off between sectors, i.e., a constant marginal rate of transformation (MRT) as labor shifts from one sector to the other. In the specific factors model, goods are produced with labor that is mobile across sectors, while some factors are sector-specific (e.g., capital is tied to the sector). The key implication is that, given fixed technology and a fixed total quantity of labor, reallocating labor changes output in a manner that, under the standard setup, yields a constant opportunity cost when measured along the PPF, producing a straight-line frontier with a constant slope for the labor allocation decision.

Option 2 analysis: A straight line with a varying shape would suggest the MRT changes as you move along the PPF, i.e., a non-constant opportunity cost. However, the specific factors model typically implies a more uniform trade-off in the labor allocation decision when technology and resource constraints are fixed, making a non-constant slope less consistent with the canonical derivation of the labor allocation path.

Option 3 analysis: An increasing hyperbolic-type curve flipped around would indicate a rapidly changing MRT as you reallocate labor, producing outputs with strong curvature in the labor allocation path. This is not a standard outcome of the specific factors framework, where the model’s structure does not naturally generate such sharp curvature in the labor allocation locus under fixed-tech and fixed-factor assumptions.

Option 4 analysis: A decreasing hyperbolic-type curve flipped around would similarly imply a highly curved, nonlinear MRT with diminishing returns in a manner not typical of the canonical specific factors setup. Like option 3, this does not align with the usual simplifications and results derived in the model when labor is mobile between sectors and capital is sector-specific, given fixed technology.

Synthesis: Across the options, the most consistent characterization with the standard specific factors model’s assumptions—mobility of labor across sectors but with sector-specific capital and fixed technology—leans toward a linear trade-off between sectors when viewed through the lens of the labor allocation decision, yielding a straight line with a constant slope. The remaining choices imply more complex curvature or non-constant opportunity costs that the basic model does not typically produce without additional structure or assumptions.

Note: If you’re reviewing this in a course, double-check the exact formulation used in your text or lecture notes, since some presentations introduce variations (e.g., different ways of normalizing factors or presenting MRT) that could affect whether the labor allocation curve is described as perfectly linear or approximated as linear under certain conditions.

econ_420_120255_249094 Lesson 4 Quiz

Given provisions of specific factors model of international trade, explain – examining the economy PPF – what the shape of labor allocation curve should be. Select one – the most appropriate answer.

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