Individuals have preferences represented by the utility function \(u^{i} = ln(x_{1}) + ln(x_{2})\) and endoments \(e^{1} = (1,0)\) and \(e^{2} = (0,1)\) , respectively.

A bank issues balances, m, in exchange for bonds, b; it sets the rate of interest and accomodates demand.

Individuals exchange commodities subject to the cash-in-advance constraint \(pz <= m\) where \(z = (...,max[z_{l},0],...)\) . Profits of the bank are distributed as dividends to individuals equally.

1. Specify the optimization problem of an individual and derive her demand for commodities, bonds and balances.

2. Compute the family of competitive equilibria for the economy.

3. Is monetary policy effective?

4. Alternatively, each individual is endowed with balances m>0, but there is no distribution of profits by the bank. Does this specification affect the effectiveness of monetary policy?