The Multiplier in the Keynesian Model

In Chapter 11 we defined the multiplier associated with any particular type of spending as the short-run change in total output resulting from a one-unit change in that type of spending.

To calculate the effect on α_is of an increase in G, we repeat the definition of α_is, Eq. (9.B.15):

where c₀, i₀, c_y, c_r, i_r, and t₀ are parameters that determine desired consump­tion and desired investment (see Appendix 9.B). If G increases by ∆G, then α_is increases by ∆G∕(c_r + i_r), so

Next, recall from Eq. (9.B.27) that, in the short run when P = P_sr, the level of

The right side of Eq. (11.C.5) is the increase in short-run equilibrium output, Y, that occurs for each one-unit increase in government purchases, G. In other words, it is the government purchases multiplier.

in desired consumption or desired investment (as reflected in the terms c ₀ and i ₀) have the same multiplier as government purchases.

Because, and,all are positive, the multiplier is positive. However,

depending on the specific values of those parameters, the multiplier may be greater or less than 1. A case in which the multiplier is likely to be large occurs when the LM curve is horizontal (that is, when the slope of the LM curve,is 0). If the LM curve is horizontal, shifts in the IS curve induced by changes in spending have relatively large effects on output. Recall that Eq. (9.B.16) gives the (negative of the) slope of the IS curve,.. Making this substitu­

tion and setting the slope of the LM curve,361" class="lazyload" data-src="/files/uch_group77/uch_pgroup317/uch_uch7363/image/image360.jpg">, at 0 yield a simple form of the multiplier:

For example, suppose that the marginal propensity to consume, c_γ, is 0.8 and that the tax rate, t, is 0.25. Then the multiplier defined in Eq. (11.C.6) is 1∕[ 1 — (0.75)(0.8)] = 1/0.4, or 2.5. If the LM curve is very steep, by contrast—that is, e_LM is large—then the multiplier could be quite small, as you can see from Eq. (11.C.5).