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In
economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...
, King–Plosser–Rebelo preferences are a particular functional form of
utility In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. * In a normative context, utility refers to a goal or objective that we wish ...
that is used in many macroeconomic models and
dynamic stochastic general equilibrium Dynamic stochastic general equilibrium modeling (abbreviated as DSGE, or DGE, or sometimes SDGE) is a macroeconomics, macroeconomic method which is often employed by monetary and fiscal authorities for policy analysis, explaining historical time-s ...
models. Having originally been proposed in an article that appeared in the '' Journal of Monetary Economics'' in 1988, the corresponding technical appendix detailing their derivation has only been published in 2002. Denote consumption with C, leisure with L and the absolute value of the inverse of the intertemporal elasticity of substitution in consumption with \sigma _c . Strict concavity of the utility function implies \sigma _c > 0. For 0 < \sigma _c < 1 or \sigma _c > 1 the utility function has the multiplicatively separable form u\left( \right) = \fracv\left( L \right) where v\left( L \right) is increasing and concave if 0 < \sigma _c < 1 or decreasing and convex if \sigma _c > 1 . Further restrictions are required to assure overall concavity of the momentarily utility function. In the limit case of \sigma _c = 1 the resulting preferences specification is additively separable and given by u\left( \right) = \ln + v\left( L \right) where v\left( L \right) is increasing and concave. The reason for the prevalence of this preference specification in macroeconomics is that they are compatible with balanced growth along the optimal
steady state In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p' ...
. Hence, they are used in many
dynamic stochastic general equilibrium Dynamic stochastic general equilibrium modeling (abbreviated as DSGE, or DGE, or sometimes SDGE) is a macroeconomics, macroeconomic method which is often employed by monetary and fiscal authorities for policy analysis, explaining historical time-s ...
models, which are typically derived from the neoclassical growth model. The reason for their compatibility with balanced growth is twofold. First, having a constant
interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...
in
steady state In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p' ...
, the growth rate of
marginal utility Marginal utility, in mainstream economics, describes the change in ''utility'' (pleasure or satisfaction resulting from the consumption) of one unit of a good or service. Marginal utility can be positive, negative, or zero. Negative marginal utilit ...
must be constant, which is the case here. Second, having a finite time endowment, balanced growth together with an optimal choice of labor by the agents implies that
income Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms. Income is difficult to define conceptually and the definition may be different across fields. F ...
and substitution effect of the increase in real wages due to
productivity Productivity is the efficiency of production of goods or services expressed by some measure. Measurements of productivity are often expressed as a ratio of an aggregate output to a single input or an aggregate input used in a production proce ...
increases must cancel each other.


Shortcut to achieve balanced growth compatibility

To have additively separable preferences along with balanced growth, some studies use the shortcut of introducing a scaling factor containing the level of labor augmenting technology before the leisure term. An example of such a utility function would be u\left( C,L \right) = \fracC^ - z^\frac Where \kappa denotes the inverse of the Frisch elasticity of labor supply and z is the level of labor augmenting technology.


Relationship to other common macroeconomic preference types

KPR-preferences are one polar case nested in Jaimovich–Rebelo preferences. The latter allow to freely scale the
wealth effect The wealth effect is the change in spending that accompanies a change in perceived wealth. Usually the wealth effect is positive: spending changes in the same direction as perceived wealth. Effect on individuals Changes in a consumer's wealth caus ...
on the labor supply. The other polar case is the
Greenwood–Hercowitz–Huffman preferences Greenwood–Hercowitz–Huffman preferences are a particular functional form of utility developed by Jeremy Greenwood (economist), Jeremy Greenwood, Zvi Hercowitz, and Gregory Huffman, in their 1988 paper ''Investment, Capacity Utilization, and the ...
, where the wealth effect on the labor supply is completely shut off. However, this naturally implies that they are incompatible with a balanced growth path.


References

{{DEFAULTSORT:King-Plosser-Rebelo preferences Neoclassical economics Utility function types