In order to solve for the time of the speculative attack, we must compute the model’s dynamic, perfect foresight equilibrium. In this section, we describe the key equations that allow us to do this.

At time 0, when information about the new fiscal deficit arrives, the representative agent re-optimizes his consumption plan. The value of the Lagrange multiplier associated with his intertemporal budget constraint jumps from A to A. The consumption optimization condition for time interval 1 is,

Since the government rebates the seignorage revenues in the form of lump sum transfers, the present value of the resources available to the consumer does not change with the arrival of new information at time zero. However, given that the rate of inflation will no longer be constant, consumption at time 0 will, in general, be different from c. The cash in advance constraint is binding, so the time 0 value of real balances must also jump from m = с to m = c. Since Pt = S before t* the change in real balances is accomplished by a change in the nominal money supply from M to M, where M is given by:

The last two terms of this equation represent the accumulated government debt up to t*. The term (M — M)/S represents the jump in the value of the debt that takes place at time zero. The term (M — M*)/S represents the discrete, positive increase in government debt that takes place at t*. This increase reflects the fact that agents trade domestic money, at the exchange rate S. for either government bonds or foreign assets. payday loans with no bank account

Equations (3.3) and (3.5) together with the cash in advance constraint imply:

In order to solve for the time of the speculative attack, we must compute the model’s dynamic, perfect foresight equilibrium. In this section, we describe the key equations that allow us to do this. At time 0, when information about the new fiscal deficit arrives, the representative agent re-optimizes his consumption plan. The value of the Lagrange multiplier associated with his intertemporal budget constraint jumps from A to A. The consumption optimization condition for time interval 1 is, Since the government rebates the seignorage revenues in the form of lump sum transfers, the present value of the resources available to the consumer does not change with the arrival of new information at time zero. However, given that the rate of