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In either regime, this solution can be obtained by combining the loan demand function (6) together with a loan supply function obtained from the first order conditions and (5).
From there, substituting (7), (3b), and (3c) into (3e) respectively for D, X, and F (including the value of zero when the given corner solution applies) and then substituting (3a) into the resulting expression for λ gives us the loan supply equations.
On the one hand, in the X = 0 and F > 0 regime, which occurs when rF > rX, the loan supply function is
On the other hand, in the F = 0 and X > 0 regime, which occurs when rF < rX, the expression for loan supply is
Inspection of the loan supply functions (8a) and (8b) reveals several interesting properties that play into the general-equilibrium solutions.
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