What Is a Monetary Model?

Monetary model is an important branch of asset market analysis in western exchange rate determination theory. The asset market analysis method is a theory of exchange rate determination that has grown rapidly from the beginning.

Currency model

Commodity prices are fully elastic, which means that when

the first,

1 Rational Expectation Model

2 Classical

Money model in utility function (MIU Model)

The currency model in the utility function was first proposed by Sidrauski (1967). The model assumes that the agent's utility comes from both the consumption of goods and the holding of money. The reason why holding money can bring direct utility is that the use of money reduces the shopping time in the "No Double Coincidence of Wants" transaction, and time can bring utility to people. However, to increase the amount of money held, it is necessary to reduce the amount of consumption or bond ownership of the actor, and these will also bring utility to the actor. Therefore, to maximize its utility, the actor needs to make a trade-off between the amount of money held and its consumption or bond ownership. If the demand for money in the model economy under steady state is positive and it can bring utility to people, then money has a positive value. The MIU model is the first model to make money truly positive in equilibrium analysis.

Contents of the currency model in the utility function

The currency model in the utility function represents the utility function of a representative actor as:

Currency model

formula

Among them, c t (= C / N ) is the per capita consumption of period t, m t (= M / P N ) is the actual currency balance per capita, and 0 < <1 is the discount factor. It is generally assumed that u c > 0, u m > 0, and u ( c , m ) are strictly concave functions. It is assumed that there are two types of assets: money and material capital in the economy. Given income, the wealth of the actor is decomposed into three parts: consumption, capital investment and currency balance. Let t be the net transfer payment that the actor received from the government in period t, t be the inflation rate, Y t be the output in period t, and be the depreciation rate of the capital. The overall economic budget limit can be expressed as

Currency model

In the formula, f ( k t 1) = y t .

The family chooses c t , k t and m t under the constraint of equation (3) to maximize the objective function (1). An analysis of this problem can

By value function. The family initial wealth w t is the state variable of the problem. The value function V ( w t ) is the present value of the utility when the household optimally selects consumption, capital stock, and money balance:

Currency model

Among them, is the marginal utility of consumption in period t. According to the envelope theorem,

t = V w ( w t ) = u c ( u t , m t )

The meaning of the first-order condition is that the initial condition is divided into three parts: consumption, capital, and currency balance. Under the optimal configuration, the marginal utility of each part is the same.

Currency model

The system describes the consumption, capital amount and currency balance selected by the actors at each point in time. This system can be used to analyze economic dynamics. For example, by analyzing the steady state, we can draw a super-neutral conclusion that the capital stock is independent of the growth rate of money and the consumption level at equilibrium is not related to the growth of money (Sidrausky, 1967). Due to the utility of money, inflation will bring welfare losses when reducing the currency balance, so that the optimal inflation rate can be found, which occurs when the nominal interest rate is zero, which is the Friedman criterion. Special setting of the utility function can be used to examine the welfare cost of inflation in a country (Lucas, 1994).

significance

The MIU model pioneered the derivation of money demand from the pursuit of utility maximization by the actor, and reached the conclusion that money demand is positive under equilibrium. However, the model assumes that the use of money can reduce shopping time without directly simulating why it would be difficult to exchange without money. In addition, the model implicitly assumes that money is the only medium of exchange, but there are no explicit restrictions in the model to achieve this. In fact, since the rate of return of money is the lowest, people can hold wealth in non-monetary form, and only exchange a part of non-financial assets into currency when exchanging. If so, people's best decision is to put all their savings on productive capital or bonds rather than money. If everyone does this, the demand for money is only positive for an instant and zero at other times.