Knowee
Questions
Features
Study Tools

Question 1 Consider the production function:F (L, K) = L13 K 23 .Suppose the wage rate (price per unit of labour), w, is 1 and, the capital rental rate (priceper unit of capital), r, is 2.(a) Does this production function exhibit increasing, decreasing or constant returns toscale? Justify your answer.

Question

Question 1 Consider the production function:F (L, K) = L13 K 23 .Suppose the wage rate (price per unit of labour), w, is 1 and, the capital rental rate (priceper unit of capital), r, is 2.(a) Does this production function exhibit increasing, decreasing or constant returns toscale? Justify your answer.

🧐 Not the exact question you are looking for?Go ask a question

Solution

The production function F(L, K) = L^(1/3) * K^(2/3) exhibits constant returns to scale. This can be determined by checking if the sum of the exponents of L and K equals 1.

In this case, 1/3 (from L) + 2/3 (from K) = 1, which confirms that the production function has constant returns to scale. This means that if we were to double both the amount of labor and capital, the output would also double.

This property is independent of the wage rate and capital rental rate.

This problem has been solved

Similar Questions

Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scaleA. Q = 10X + 4Y + 0.25ZB. Q = 12L + 5K + 500C. Q = 4A + 14B + 3ABD. Q = 5L2 + 5LK + 5K2Which production function exhibit constant returns to scale?a.Cb.Bc.Ad.DWhich production function exhibit increasing returns to scale?a.A and Bb.C and Dc.D and Ad.B and CWhich production function exhibit decreasing returns to scale?a.Ab.Cc.Bd.D

The production function will shift up as a result ofResponsesA increasing returns to labor.increasing returns to labor.B diminishing returns to labor.diminishing returns to labor.C an increase in capital input.an increase in capital input.D a decrease in capital input.

If the slope of a total production function decreases as one input increases, the firm's underlying production function exhibits:a.increasing returns to scale.b.constant returns to scale.c.decreasing returns to a factor input.d.decreasing returns to scale.

Consider the aggregate production function Y = 3K0.6N0.3, which of the following observations is incorrect?Group of answer choicesThe production function exhibits decreasing return to capital.The production function exhibits constant returns to scale.The production function exhibits decreasing return to labour.All other observations are correct.

Consider the following figure:The shape of this production function suggests:a) a constant marginal product of capital.b) a diminishing marginal product of capital.c) a diminishing marginal product of labour.d) an increasing marginal product of capital.e) Not enough information is given

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.