Consider the formal moments of the game. We introduce the basic definitions:
- the level (rate) of inflation: ;
- the expected level (rate) of inflation: ;
- the growth rate of the money supply: ;
- real wages: ;
- Employment: .
Let's initially . Then .
We will assume that inflation is an exclusively monetary phenomenon:
and the economy is dominated by free competition.
The strategy of the game participants is as follows:
- the central bank chooses the value - is responsible for monetary and pricing policies, for inflation targeting;
- Employees sign a contract for - the nominal value of wages;
- firms determine the level of aggregate employment in the economy I.
Rewards agents can be represented in this way.
The optimal labor supply is a function of the form , where α is the elasticity of labor supply relative to real wages.
The goal of employees is to minimize the difference between real employment (chosen by firms) and optimal employment (maximizing their utility function). In other words, their goal is to maximize their utility function:
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which can be written as a welfare function (an indirect utility function):
The result of the game for employees is a certain level of well-being.
Choose the target values for inflation - - and the level of employment - .
The Central Bank's objective function can be represented as:
Deviation squares mean that the more in any direction the actual indicator deviates from the target one, the higher the marginal losses of the aggregate welfare (the aggregate utility of the population of the country).
The μ parameter shows the relative importance of the inflation and unemployment targets: 0 & lt; μ & lt; 1.
The goal of the Central Bank is to maximize its objective function, to minimize welfare losses for the economy as a whole.
Firms choose actions that maximize their profits. According to the conditions of free competition, they are price-recipients in the food and labor markets. Firms are guided by the marginal profitability rule: .
Then the optimal demand for labor (maximizing the profits of firms) can be represented in the form
where k - the elasticity of the demand for labor relative to the real wage rate.
The real demand for labor is:
The purpose of firms is to minimize the difference between real employment and optimal labor demand.
The target function of the firms will then look like this:
The square of the deviation and here shows the growth of marginal losses with an increase in the difference between real and target values.
So, we now have three strategies and three objective functions of participants in the monetary economic process. Consider the mechanism of the game.
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