In an economy, there are two types of firms: 50% of firms are risky (type 1) and 50% are safe (type 2).To start operating, each firm needs to invest10monetary units with its own resources and borrow10monetary units from a competitive and risk-neutral bank (with zero expected profit).Firms know their own type.

Once operating,ariskyfirmhas a 20% probability of success, in which case it has a production of120currency units.With an 80% probability, ariskyfirmfailsand has zero production.

A secure firm, on the other hand, is80% successful,in which case it produces30monetary units.With a 20% probability, asafefirmfails and has aprofitof zero.

After production is completed, a firm only pays the bank if it succeeds.The bank charges a conditional payment on success that earns youan expected amount of10(note that as there is only payment in case of success, the payment in this contingency must be greater than10).

The profit of a firm, in the case of success, is the value of its production, less the10monetary units anticipated in the first period less the amount paid to the bank.Thus, for example, a risky firm, under success, has a profit of110-P, with P being the amount paid to the bank.Under failure, both types of firms have aprofitof-10(corresponding to investment losses in the first period).Both firmsare risk neutral,which means that, ex-ante, they make their decisions in order to maximize the expected profit.

(a)What is theexpectedproductionof each type of firm?(Hint: you'll see that both types will have the same expected output)

(b)Suppose the bank looks at the type of firm.Show that the bank will charge12.5monetary unitsfrom type 2firmson success.

(c)Still assuming that the bank observes the type of firm, what will be the amount chargedfor type 1in case of success.