Why do you think this might lead to proble 2 The Too Big To Fail subsidy and

Why do you think this might lead to proble 2 the too

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in”). Why do you think this might lead to problems ? 2 . The ‘Too Big To Fail’ subsidy and bank leverage Consider a bank that has one unit of shareholder equity and can also borrow additional funds, 𝐵 , on which it promises to pay 𝑅 to the depositors/bond holders (NB: 𝑅 is the total return, i.e. it includes the repayment of the principal as well as interest paid). The bank then uses its funds to make loans 𝐿 (so 𝐿 = 1 + 𝐵 ). Because it becomes progressively harder for the bank to find good projects the more loans that it makes, the return on these loans declines with the quantity of loans issued. The rate of return on loans is 6 √𝐿 . a. Write down an expression for the bank’s profits and derive the first-order condition for the optimal volume of loans extended and funds borrowed. If the total return on safe assets (e.g. a government bond) is unity, what value must 𝑅 take in a competitive market? Using your result, what is the volume of loans extended and funds borrowed?
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2 b. Now suppose that there is uncertainty over whether the loans can be repaid or not (you should think of this as macroeconomic risk affecting all the loans, rather than idiosyncratic risk that affects only some of them). In particular, the loans default in their entirety with probability 1/3
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