836
A. G. MALLIARIS
2. Generalized Deflationary and Inflationary Gaps
     We begin this section by introducing the concept of full employment labor force, Lt. Let Ls denote the total labor which is the available labor supply at a given period and assume that 4% of this total labor force could not be employed because of frictional unemployment. Then we have the relationship of equation
(19)                       L, = (1 - .04)1,.
     Corresponding to the level of the full employment labor force we have the concept of full employment total real output, Yh which is defined to be that level of total real output which could be produced if the level of full employment labor force were combined with a given level of capital stock and other given factors such as technology, expectations, resources, etc. In equational form we have
(20)                       Y, = Y(Lt,K,U),
where K and U are assumed to be constant quantities (5).
     The definition of the generalized deflationary gap, g. d. g., is given in equation
(21)                  g.d.g. = min {r(T,)} ~ d(Yt),
where min means minimum value of the dependent variable of the aggregate supply function when the independent variable takes the value Y/(6).
     (5)     For a different definition of full employment output see B. Hickman et al., « The Hickman-Coen Annual Growth Model: Structural Characteristics and Policy Responses», International Economic Review, February 1975, p. 25.
     (6)     This definition implies that the g.d.g. measures the gap between the price level at which the full employment output is supplied and the price level at which the full employment output is demanded. An alternative definition that would measure an output gap instead of a price gap would be
(21a)                                g. d. g. = Yf - Yd ,
where Yd is obtained as follows: let P'1 = min {r(Y/)}; then there is an output level, say Yd, such that Pd = d (Yd). However, this latter definition is not consistent with the definition of d.g. because equation (21a) corresponds to the output gap, Yf - Ye, where Ye is the equilibrium nominal income. Of course, in the national income model the d.g. and the output gap are two distinct concepts. For this reason we have adopted the price gap definition of equation (21). It is worth noting that a third definition has also been considered i.e.,
(21b)                              g d.g. = (Yf - Y0)/mg,
i.e., the g.d.g. is defined as the ratio of the real output gap, with Y0 being an equilibrium total real output less than Yf, to the government spending multiplier, mg. The difficulty with (21b) is that the g.d.g. would have different magnitudes depending on whether we use