Question

Plot an Isocost line for a firm that is spending $10,000 on labor and capital. Then, draw a Cobb-Douglas Isoquant for this firm that intersects your Isocost curve. Label the two intersection points A and B. Draw a second Isosquant that is just tangent to the Isocost curve, and label the point of tangency point C. Explain why it would not be efficient for this firm to produce at point A nor point B.

Answer 1

To know why it is not efficient to produce to either A or B, we have to know what Isoquant and Isocost line means.

Firstly, Isoquant means the different possible combinations of labor and capital that can produce the same constant output. Thus along with an Isoquant, the quantity remains constant. Now higher the isoquant (shifting towards Isoquants of more away from the origin), represents a higher level output because the higher Isoquant contains both more labor and more capital and thus able to produce more output. Here it can be seen that in our figure the isoquant which passes through point A & B contains less labor and capital than the isoquant that passes through point C, so naturally, the isoquant which passes through point C represents a higher level output than the isoquant that passes through points A & B. But one thing we must have to keep in mind that the output level along with the isoquant that passes through points A & B is constant and the isoquant that passes through point C just represents another level (higher than the previous one that passes through A & B); but the output along with this isoquant is fixed too.

Secondly, the Isocost line means the different possible combinations of Labor and Capital that produces the same fixed cost to the producer. Similar to the Isoquant, higher the Isocost cost line (Shifting towards Isocost line more away from the origin), higher the associated cost of production, and along with an Isocost line the cost of production remains constant.

Now, in our figure, the isocost line represents different combinations of Labor & Capital that yield a fixed production cost of $10,000.

As we have already discussed the Isoquant that passes through point C represents a higher output level than the isoquant that passes through A & B. Thus if the firm operates at Point C, it can produce a higher output level with a cost of $10,000 (since at point C this Isoquant is tangent to the Isocost line of $10,000). Hence, it is not optimal for the firm to produce a lower output put by operating either at Point A or at Point B and incur a same amount of cost of $10,000.

This is why it is not efficient for the firm to produce either at Point A or at Point B.