Notes on Liquidity Traps with Cash-in-Advance

where 0    1 0    1  is consumption of goods which can be purchased only with money, and  is consumption of goods that can be purchased with government bonds or with money. Again, this is pretty crude, but we could put banks in the model, for example, which hold government bonds, and then bank deposits backed by government bonds are used in exchange — essentially the same thing. I’m assuming constant marginal disutility of supplying labor,  where   0 I don’t think I need this, but it makes life easier. The production technology is simple: one unit of labor produces one unit of either consumption good. Suppose that production takes place at a representative firm. The equilibrium real wage is  = 1 At the beginning of period  the representative agent has  units of money balances, and  one-period government bonds (both in units of the period −1 consumption good 1). The agent receives the payoff on government bonds in money, trades on the asset market, and receives a lump-sum transfer   from the government. The asset market constraint for the agent is