Suppose demand for widgets is given by P=100-Q, where P is the market price and Q is the market supply (which is the sum of total production in the market).

There is an incumbent widget firm who has a cost function given by C(qi)=100+20qi,. There is a potential entrant deciding whether or not enter the market.

The cost function of the potential entrant is C(qe)=100+30qe. The timeline of the game is as follows.

In stage 1, the incumbent firm decides and announces qi,, which cannot be changed after the announcement

In stage 2, the potential entrant observes the announces of the incumbent firm, and then it decides whether enter or not.

In stage 3, if the potential entrant decides not to enter, then the incumbent firm is still the only firm in the market and produces what it has announced in stage 1. If the

potential entrant chooses to enter, then it chooses how much to produce qe, and the incumbent firm produces what it has announced in stage 1.

Note: Input numerical answers only. Do not input notations such as "$" and ",". For fractions such as one-half, write it as 0.50 rather than 1/2. Please keep 2 decimal places

in your answers.

a) [2 marks] If there was no potential entrant at all, how much should the incumbent firm produce?

How much would be the consumer surplus?

b) [3 marks] If the incumbent accommodates entry (i.e., expecting the potential entrant to enter), then how much should the incumbent produce?

How much

would be the consumer surplus?

c) [3 marks] If the incumbents wants to block the entry (so that it can still be a monopolist), how much should it produce?

How much would be the consumer

surplus?