Question

Suppose that the home country has an endowment of 64 units of labor, which can be used to produce produce goods X and Y. Good Y is produced by a competitive industry under constant returns to scale, with a

LY = 1 the labor requirement per unit of good Y. The X industry is a competitive industry with increasing returns that are external to the firm. The unit labor requirement for producing X is a LX =.5L−¹/³ₓ , where LX
​is the total employment in the X sector.
a) Draw the industry level relationship between output and labor for the X sector, and use this to draw a production possibility frontier for the country. For what world prices would the home country be best off by specializing in good X ?

Answer 1

The country has 64 units of labor and produces goods X and Y, with Y having constant returns and X having increasing returns to scale. A production possibility frontier can be drawn to show the trade-offs, and the country benefits from specializing in good X if world prices provide a comparative advantage, as economies of scale mean lower average costs and higher output.

Step-by-step explanation:

In economics, when considering the production of goods, we often use models to help understand trade-offs and production capabilities. In the scenario provided, we have a country with 64 units of labor able to produce goods X and Y. Good Y operates under constant returns to scale with a labor requirement of one unit per good. However, the more interesting case is good X, which is produced under increasing returns to scale, with a labor requirement expressed by the function LX = 0.5L^(-1/3), where LX represents the total labor employed in the X sector.

The relationship between output and labor for good X exhibits economies of scale, meaning as output increases, the unit labor requirement decreases. To visualize this, one would plot the labor units on the x-axis and the output on the y-axis to create a curve that shows increasing output for each additional unit of labor at an increasing rate. When combined with the linear production of good Y, this relationship can be used to construct the country's production possibility frontier (PPF). This graphically represents all possible combinations of goods X and Y that the country can produce, given its labor constraints.

Regarding trade, the home country would be best off specializing in good X when the world prices indicate a comparative advantage in producing X, which is determined by the price of X being high enough relative to the price of Y to offset the increasing returns to scale in X. When economies of scale are present, as in the production of good X, specialization can lead to significantly lower average costs and higher outputs, and therefore, for certain world prices, specializing in X can be much more profitable than producing both X and Y.