MIU model

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The MIU model ( money-in-utility-function model , for example model with money in the utility function ) assumes that the real money supply (per capita) is an argument of the utility function . Accordingly, money creates a direct benefit (similar to normal goods ) .

This approach was proposed by John R. Hicks and elaborated extensively by Don Patinkin and Miguel Sidrauski .

A related approach is the CIA ( cash-in-advance ) model.

Basic problem

The MIU model serves, among other things, as an extension of the neoclassical Solow model that describes a non-monetary economy. Goods are exchanged and transactions are carried out here, but without a medium of exchange. In order to examine monetary aspects it is necessary to specify why people hold a positive amount of money (compare money demand ).

The MIU model is thus an answer to the theoretical challenge of designing a general equilibrium model in which money is not included in the preferences , but nevertheless has a positive value in equilibrium. Since money has no intrinsic value (“money cannot be eaten”) it probably does not appear in the utility function (like other economic goods ). Based on Frank Hahn , this fundamental problem is also referred to as the Hahn problem .

model

The starting point is a utility function with positive, decreasing marginal utility . In addition, future benefits are discounted by a factor (see time preference ). It is also assumed:

  • The production function is: where capital at a rate depreciated is.
  • Profits from capital are given by: .
  • And there is a gross nominal rate of .

The budget constraint can then be formulated as follows:

On the left side of the equation is the household income in the period : production, any transfers and financial assets (interest-bearing money or securities). On the right side are the real values at the time : the per capita consumption ( ), the cash keeping ( ), the capital acquisition ( ), and the securities ( ) the expenditure of the household. This relationship applies in every period. The aim of the budget is to maximize utility while taking this budget restriction into account. The control variables are accordingly .

The result shows the relative costs of holding money:

On the left is the marginal rate of substitution between money and consumption. The right side describes the relative price ( opportunity cost ) of holding money expressed in units of the consumer good. The opportunity cost is , but will not be paid until the next period. Therefore, the discounted opportunity costs are as follows: .

Alternative modeling

The chronological order of the money utility can easily be changed. Carlstrom and Fuerst (2001) suggested that money only creates utility if it is available before consumer goods are bought. An alternative modeling changes the opportunity costs in the equilibrium of the MIU model.

Results

Under the MIU assumption that money is of direct benefit, inflation always causes a loss of welfare because it reduces the real value of money. The private opportunity costs of holding money depend on the nominal interest rate. If the nominal interest rate is zero, there is deflation roughly in the amount of investment income (see Fisher equation ).

Robert E. Lucas (1994) dealt among other things with the loss of welfare due to inflation. He also conducted empirical studies based on US data from 1900 to 1985. According to this, a nominal inflation rate of 10% would result in an annual welfare loss (in the form of lost consumption) of US $ 32 billion.

On the other hand, Laurence Ball was concerned with the question of how expensive it would be to reduce inflation. He reports a tradeoff of 2.4 percent in production that would have to be abandoned in order to reduce inflation by 1 percent.

Overall, the MIU model also demonstrates the property of money's super-neutrality : money supply growth and inflation have no effect on real variables such as capital intensity and per capita consumption. Under certain conditions, money is not neutral.

Individual evidence

  1. ↑ a b Engels, Roland. For the microeconomic foundation of the money demand in general equilibrium models. Univ. Passau, 2004. p. 21. Online PDF
  2. ^ Walsh, Carl E. Monetary theory and policy. MIT press, 2010. p. 33.
  3. ^ Comparison: Hahn, Frank H. "On some problems of proving the existence of an equilibrium in a monetary economy." The theory of interest rates (1965): 126-135.
  4. ^ Walsh, Carl E. Monetary theory and policy. MIT press, 2010. p. 37.
  5. ↑ Lucas, Robert E. On the welfare cost of inflation. No. 394. Center for Economic Policy Research, Stanford University, 1994.
  6. ^ Walsh, Carl E. Monetary theory and policy. MIT press, 2010. pp. 55/56.
  7. ↑ Ball, Laurence. "How costly is disinflation? The historical evidence." Business Review Nov (1993): 17-28. P. 18
  8. ↑ monetary growth theory - article in the Gabler Wirtschaftslexikon.
  9. ↑ J. Benchimol, A. Fourçans: Money and Risk in a DSGE Framework: A Bayesian Application to the euro zone . In: Journal of Macroeconomics . 34, No. 1, 2012, pp. 95-111. doi : 10.1016 / j.jmacro.2011.10.003 .
  10. ↑ J. Benchimol: Money in the production function: a new Keynesian DSGE perspective . In: Southern Economic Journal . 82, No. 1, 2015, pp. 152-184. doi : 10.4284 / 0038-4038-2011.197 .
  11. ↑ J. Benchimol: Money and monetary policy in Israel during the load decade . In: Journal of Policy Modeling . 38, No. 1, 2016, pp. 103-124. doi : 10.1016 / j.jpolmod.2015.12.007 .

literature

  • Sidrauski, Miguel. "Rational choice and patterns of growth in a monetary economy." The American Economic Review (1967): 534-544.
  • Walsh, Carl E. Monetary theory and policy. MIT press, 2010. Chapter 2.

Web links

  • Benefit of money - definition in the Gabler Wirtschaftslexikon
  • Money theory - including money demand theory in the Gabler Wirtschaftslexikon