Question

In: Economics

A competitive firm has a production function ?(?, ?) = (? + ?)1/2 where ? and...

A competitive firm has a production function ?(?, ?) = (? + ?)1/2 where ? and ? stand for inputs capital and labour respectively. The price of capital is ?, and the price of labour is ?. Which of the following is true?

  1. Regardless of ? and ?, cost minimisation requires that ? = ?.

  2. If ? > ?, contingent demand for labour is 0.

  3. The technology has increasing returns to scale.

  4. If ? < ?, profit maximisation requires that no labour is used in production.

Solutions

Expert Solution

From the above analysis we know that:----

if w > v => contingent demand of capital is greater than zero & contingent demand of labor is 0.

if w < v => contingent demand of labor is greater than zero & contingent demand of capital is 0.

if w = v => contingent demand of both capital & of labor is greater than zero.

Hence only D is true as A & B cannot be true due to above analysis.

Also f(tK,TL) = (1/2)(tK + tL) = t*[(K+L)/2] = t*f(K,L) => constant return to scale. hence C is also false.

only D is true.

Rahul Sunny answered 2 years ago
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