Monetary Discretion, Pricing Complementarity and Dynamic Multiple Equilibria

(i) The left side is strictly concave and increasing; the right hand side is strictly
increasing (since ε > 1), and either strictly concave (if ε < 2) or strictly convex (if ε > 2).

(ii) LHS → -∞ as po → 0⁺, and lim LHS = m*.

(iii) RHS (0) = 0.RHS→∞as p^p0⁰→∞.

(iv) Thus, this equation has either two solutions or no solutions.

(v) Can show there is a unique m, call it m such that LHS and RHS are tangent.

(iv) As m increases above fh, solution disappears; as m decreases below fh two solu-
tions emerge ■

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