Question

In the context of our analysis of the Edgeworth production box, suppose that a new invention changes a constant-returns-to-scale food production process into one that exhibits sharply increasing returns. How does this change affect the production contract curve?

Short answer

If a new invention would change the constant returns to scale to increasing return to scale, this will not affect the production contract curve.

Step-by-step solution

Step 1. No effect on the production contract curve

We know that an Edgeworth production box depicts the production contract curve, which results from tangency between the different points on the isoquants of the individual production processes.

If supposedly there is a change from a constant-returns-to-scale production process to a sharply-increasing-returns-to-scale due to a new invention, this will not necessarily change the shape of the isoquants. It is because the marginal productivity of the inputs will remain the same, there will be no change in the marginal rate of technical substitution.

We know that the shape of the contract curve depends upon the marginal rate of technical substitution between two goods. Since we have already established that the MRTS will not change due to change in return from constant to increasing, we could conclude that the shape of the production contract curve would remain the same, and there will be no effect of this change.

For example: Consider Y=LK changes to Y=L2K2

In both cases, the MRTS=K/L, hence there is no change in the production contract curve.

The change can be seen only because of the change in the trade-off between the used inputs (affecting the shape of isoquant)