As in Variant 4 of the ABT model, instead of setting the real brokerage fee b equal to a constant that is independent of the real cash withdrawal c as in ABT, allow b to increase with c as follows: b = b(c) = b0ca for 0 < a < 1 and some constant b0 > 0. (a = 0 in ABT).

a) (15 points) What is real money demand, in terms of real transactions t, the nominal interest rate i, b0, and a? Show your derivation, using back of page or an additional sheet if necessary.

b) (10 points) What are the transactions and interest elasticites e and h as a function of a? In what ranges must these lie?

c) (5 points) What is mD in the limit a 1? Explain briefly. (Hint: How does the constant in mD behave as a 1? ) As noted in the lecture, Baumol (his footnote 4) considers the affine form b(c) = b + kc, and finds that k > 0 has no effect. Evidently the curvature of the dependence on c is important!