Question

Suppose there is a market with a big firm and many small price-taking firms (DFCF). Given that the inverse market demand function is ?=100−??p=100−Qdand the inverse supply function for small firms is ?=40+???p=40+Qcf, calculate the output level where the residual demand function has a kink.

Answer 1

The Market demand function is p = 100 - Qd , the supply function of many small fringe firms is p = 40 + Qcf.

Now, the residual demand is the remaining market demand which will not be supplied by many small fringe firms.

The residual demand will have a kink in that output below which small fringe firms will not be able to supply in the market.

So, the Price at which the supply of small fringe firms is zero is p = 40.

Because supply function of small fringe firms is p = 40 + Qcf

If Qcf = 0, then p must be = 40.

At p = 40, Market demand is p = 100 - Qd , putting p = 40, we get Qd = 60.

So, at output level Q = 40 units the residual demand function must have a kink.

Below the price level = 40 i.e after the output level Q = 60, the residual demand is same as market demand. The kink of residual demand function will take place at Q = 40. (Ans).