QUARTERLY JOURNAL OF ECONOMICS satisfy homogeneity; when nominal prices double, so does the ASSUMPTION 2. Symmetric Price Index. The aggregate price index Q(t)depends only on the frequency distribution of nominal prices and satisfies homogeneity: (2)Q(t)=Q(G,(q)), where G (q)is the proportion of firms i∈[0,1 such that q:(t)≤q, 3)if G, (q)-GL (q) for all q, then xQ(t,)-Q(t2), for any ti, t2 20 This condition is satisfied by a wide variety of common price indices.An example of a price index that satisfies Assumption 2 is a simple average of nominal prices based on their frequency distribu tion,Q(t)=adG (q). More generally, let Q(t) w(q, G ())qdG (q), where w(, G)represents weights as a function of prices q and the distribution of nominal prices G. The assump tion requires the weights to satisfy w(q, G, )-w(g, Gi, ) when G, ( q)-G (q) for all q. An example of such a set of weights is w(q, G)-ql/ adG(q) IIB. The Market Setting Consumer demand is assumed to depend only on the firm s real price and on real money balances. Writing the arguments in log form, consumer demand faced by firm i, Ti, is defined by Ti (t)=r(r: (t), M(t)-P(t)), where r (t)and M(t)-P(t)are the log of firm i's price and the lo of real balances, respectively. One rationale for this is to assume that real balances enter consumer utility functions, as in, for example, Rotemberg [1982, 1983]. Note also that all firms can have Individual firms set s and S taking the price level as exogenous S, the index endogenously determines P(O O)relative to the exe 4. Blanchard and Kiyotaki [1985]and Ball and Romer 1986] derive symmetric price indices based on an underlying symmetric utility framework dependent of future prices rules out Benabou [1985a real money balances may also influence real demand. For present purposes, Proposition 1 will allow us to ignore this potentially complex depender706 QUARTERLY JOURNAL OF ECONOMICS satisfy homogeneity; when nominal prices double, so does the index.3 ASSUMPTION2. Symmetric Price Index. The aggregate price index Q(t) depends only on the frequency distribution of nominal prices and satisfies homogeneity: (2) Q (t) = Q (G,(q)), where Gt(q) is the proportion of firms i E [0,1] such that q,(t) i q, (3) if G,,(q) = Gt2(hq) for all q, then XQ(t,) = Q(t,), for any t,, t, r 0. This condition is satisfied by a wide variety of common price in dice^.^ An example of a price index that satisfies Assumption 2 is a simple average of nominal prices based on their frequency distribu￾tion, Q(t) = fqd~t(q).More generally, let Q(t) = f w (q,Gt(. ))qdGt (q), where w (q,G) represents weights as a function of prices q and the distribution of nominal prices G. The assump￾tion requires the weights to satisfy w(q,GtI) = w(hq, G,,) when Gtl(q) = Gt2(Xq) for all q. An example of such a set of weights is w(q,G) = q/f qdG(q). IIB. The Market Setting Consumer demand is assumed to depend only on the firm's real price and on real money balances. Writing the arguments in log form, consumer demand faced by firm i, ri, is defined by (4) r,(t) = r(ri(t), M(t) -P(t)), where ri(t) and M(t) -P(t) are the log of firm i's price and the log of real balances, re~~ectively.~ One rationale for this is to assume that real balances enter consumer utility functions, as in, for example, Rotemberg [1982,1983]. Note also that all firms can have 3. Individual firms set s and S taking the price level as exogenously given. However, for given levels s and S , the index endogenously determines P(0):will the exogenous and endogenous indices be consistent? The answer is generally no: however, if we associate higher real balances with higher levels of s and S , there will be some initial specification of real balances guaranteeing this static consistency, since higher real balances raise the desired average real price, raising the endogenous level of P(0)relative to the exogenous level. 4. Blanchard and Kiyotaki [I9851 and Ball and Romer [I9861 derive symmetric price indices based on an underlying symmetric utility framework. 5. The assumption that demand is independent of future prices rules out consumer speculation. Benabou [1985a] presents an analysis of optimal pricing policies in the face of consumer storage and speculation. In principle, the future path of real money balances may also influence real demand. For present purposes, Proposition 1will allow us to ignore this potentially complex dependence