Question

Suppose a firm ”moves” from one point on a production isoquant to another point on the same isoquant. For each of the following, briefly explain why it is always true, always false, or uncertain without further information:

1) A change in the level of output

2) A change in the ratio in which the inputs are combined

3) A change in the marginal products of the inputs

4) A change in the rate of technical substitution

5) A change in profitability

The correct answers are always false for 1, and uncertain for 2-5 but I can’t figure out why? (Professor's answers)

Edit: 1 is definition of isoquants; 2-cobb douglas makes true, negative input (diagonal line from origin) allows a constant ratio; 3-cobb true, perfect subs false; 4-same as 3; 5-need cost function to tell

Answer 1

1) The statement is false since the movement is on the same isoquant which means that only the combinations of the inputs might have changed the output is the same as long as the isoquant is the same. If the isoquant is at higher level, output increases

2) In cobb Douglas since the graph is a rectangular hyperbola , the chnage in inputs would be there depending on the direction in which the new point is. So for Cobb Douglas it is true , but it is not always true.

In case of perfect substitutes, the graph is a straight line joining both the axes. The units of inputs would have no change because they are always substitutes. So it is false in this case.

Hence it is uncertain

3) marginal products would change in case is Cobb Douglas ie the change in output when one additional unit of input is employed. It would increase, decrease depending on the units is input added so ihe statement is true. Whereas in Perfect substitutes the marginal product does not change because the inputs are perfect substitutes, so any additional increase in input increases output. So its false for this case.

Overall it's uncertain

4) Technical substitution would change in case of cobb Douglas because it is rectangular hyperbola. In case of perfect substitutes, the technical substitution rate is constant irrespective of combination of outputs. So for perfect substitutes it is false.

Hence answer is uncertain.

5) A change in profitability would be the revenue less of costs which would also depend on the isocost curve. So it is uncertain whether the profitability changes or not.

(You can comment for doubts)