these real quantities can be converted to nominal quantities by multiplying by P. So, for example, if P = 2 and C = 2, then the dollar value of consumption is 4. In what follows, we will assume a two period model (t and f + 1). The period f flow budget constraint for the household is given by: Pect + Pist + M. Spin, No - PIT, + p.D. The period f + 1 flow budget constraint for the household is given by: Notice we are imposing the terminal conditions: st+1=0 and Mr+1 = 0, since we are not allowing the house- hold to die with neither savings nor money holdings. Next, we can divide both budget constraints by the price level in order to have them expressed in real terms: MINI - T,+ D. M Pr+1 Pr+1 The term is referred to as Real Money Balances Let's take a closer look to the right hand side of the f + 1 budget constraint: The term (1 + i) , that's multiplying S,, represents the (gross) real return on saving (either through bonds or simple demand deposits). As such we will define: Itr = (1+i)-P This is known as the Fisher Equation' which, after some algebra (in the whiteboard) can be re-expressed as: Using the Fisher equation, we can re-write the budget constraint in f + 1 as follows: And get a clean expression for savings:Cr+1 1 1+r 1 +r With this, we can finally consolidate the budget constraints into one single inter-temporal budget constraint: WIN+1 - Thi+ Dr+1 MI C + + 1+r = WIN - Ti+ D: 1 +r The household's problem is thus: Max U = 1(c) + + fu(c+1) s.t inter-temporal budget constraint Notice that we are making the simplifying assumption that the household's labor supply is fixed (so labor/leisure doesn't enter as an argument into the utility function). We will also assume an endowment economy (meaning hat there is no production technology and no profits, so D, = 0 Vi) and no-government (so Tr = 0 Vr). Finally, et's assume that both the utility function and the utility of real money balances is of the following form: I (c) = 1 - Now let's go through the algebra of the model and derive the money demand function (in the whiteboard)Exercise 1: Money Demand Consider a two-period, general equilibrium, endowment economy with no government and fixed labor supply (just like the one we studied in class). There is a representative household that consumes and holds real money balances. The household's preferences are given by the following utility function: 1= T +w[%]\"+f'\" t T1-v 1-r The household's budget constraints at periods t and t+1 are: prce + pese + M,