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22) 1 b¯ = m1 + m2 − b = m2 + ( )m1 2+λ 1 m1 . 24) We now are in a position to show how to calculate λ. 5), b . 19), we have p = (1+λ)b , which is which implies that p2 p¯ = a−q b¯ ap − b¯ = (1 + λ)b, or p= a− p (1 + λ)b + b¯ m1 + m2 + λb = . 19), we may arrive at p¯ = (1 + λ)b¯ + b m1 + m2 + λb¯ = . 26) 1 equation, obtaining Now we can substitute into the p p¯ = 1+λ m1 + m2 + λb m1 + m2 + λb¯ 1 · = . 27) ¯ obtaining a fifth-degree Finally, we can use our expressions for b and b, equation for λ in terms of the input parameters m1 , m2 , and a.
10577a. 16527a—it is in the monopolist’s self-interest to make sure that money is short (competition could weaken this; Shubik, 1976). A natural question to ask is: How much of a profit can the monopolist extract from the traders as a function of the amount of money they have? , solutions where the bank is altruistic). 3. 7 A slightly more general model is presented and solved in Chapter 13. Trade with a Rich Large Agent there an amount m such that if each trader type had that amount of money, the profits of the monopolist would be maximized?
Notice that the argument for is vector-valued, with at least a component for each type. controlling the rate of interest Instead of utilizing the quantity of money as its control variable, the bank could use the rate of interest. The traders’ optimization problems are then denoted by ρ and ¯ ρ , defined in the obvious way. The bank then solves max (arg max ρ≥0 b,d ,q≥0 ρ , arg max ¯ ρ ). 10) The nonnegativity of ρ guarantees that the bank will not operate at a loss. the money supply or the interest rate?