Answer to Question #247169 in Microeconomics for Chilu

Question

Use the connection between your box diagram and the production possibility frontier to discuss what the frontier would look like in the following cases: i. Production of good X uses only labor, production of good Y uses only capital. ii. Both X and Y are produced using K and L in the same fixed proportions as the inputs are available in the economy and both exhibit constant returns to scale. iii.Both X and Y have the same production function and both exhibit constant returns to scale. iv.Both X and Y are produced using the same production function and both exhibit increasing returns to scale

Answer 1

i. If only labor is used, then the LL line reflects the boundary of the production set. If only capital is used, then the boundary is characterized by the KK line:

ii.

The constant return on scale is characterized by a simultaneous and proportional change in the factors of production involved in turnover and production volumes. That is, a firm that decides to expand production (maybe this is due to increases in the structure of demand) and increases its scale, say, twice, respectively, produces twice the volume of goods, works, services, and its production function in this case is written as follows: 2Q = (2L; 2K). It turns out that in order to get a larger volume of output, it is necessary to proportionally increase the consumption of factors of production, and how many times it changes, the result of economic activity will increase so much. At the same time, the marginal costs or marginal costs that arise with the production of each additional unit of production do not change and amount to a specific amount

iii.

The production function has a constant return on scale if the relative increase in all factors of production by the same amount leads to a relative increase in the volume of output by the same amount.

iv.

In the case when a proportional increase in the number of all applied factors n times will cause an increase in production more than n times, there is an increasing return on scale, i.e.

Q₂ > n x Q₁