Lt = L<sup>1</sup> 1<sup>�</sup> ;t<sup>�L</sup> 2<sup>�</sup> ;t<sup>.20</sup> Retailers convert intermediate goods into ...nal goods. Final output, Yt<sup>f,is</sup> produced by a continuum unit of retailers, l, who buy di¤erentiated intermediate goods, Yt, at price Pprice<sup>int</sup> inPl;ta.competitiveAggregate ...nalmarket,outputdi¤erentiateand pricesit atarenoYt<sup>f</sup> cost,= (Rand 10<sup>Y</sup> l;tsell��� <u>1</u> dla)variety��� 1 andofP...nalt = (output,R 10<sup>P 1</sup> l;t<sup>��</sup> dlYl;t) 1,�1at� , where �> 1 is the elasticity of substitution among varieties. Each retailer takes into account that it may not be able to change their price with probability �p when choosing the optimal price. Then prices are sticky à la Calvo and retailers face a downward sloping demand curve for their variety. ^ ^ This optimization problem leads to a standard New Keynesian Phillips curve �t = �Et�t+1 � �X<sup>^</sup> t, where a hat (^) denotes a log deviation from steady-state. Variables � and X = �= (� � 1) represent the in‡ation rate and average mark-up. The parameter � = (1 � �p)(1 � ��p)=�p captures the slope of the Phillips curve that determines the responsiveness of in‡ation and output to demand shocks. The higher the price stickiness (i.e., the larger �p) the more ...rms are not able to change prices to the desired level and, therefore, demand shocks generate a larger response on output. When prices are ‡exible (i.e., �p = 0 or � ! 1), demand shocks only a¤ect prices.

The relative price of intermediate goods is de...ned as the inverse of the retailer’s average markup, Pt<sup>int</sup> =Pt = 1=Xt. Then, the marginal product of labor and capital in terms of intermediate goods must be divided by the markup to generate the real marginal product.<sup>21</sup> Aggregate real wages are then given by w1t = (1 � �)(1 � �) (1=Xt) (Yt=L1;t) and w2t = �(1 � �) (1=Xt) (Yt=L2;t).

In steady state, the HtM household receives a share � of labor income, due to the Cobb-Douglas speci...cation. In order to simplify the steady state, it is assumed that the HtM household receives a transfer � of capital income and retailer’s pro...ts and pays a share � of government spending. Therefore, the HtM household accounts for a share � of total consumption.

# 3.3 Sticky wages

Workers are able to set their wages at a steady-state markup above their marginal rate of substitution �w = �w= (�w � 1), which implies that individuals have market power in their labor supply decisions. The labor supply of Ricardian and HtM households are composites of di¤erentiated labor inputs: 1 1 L1;t = R0<sup>L1;t(i)diandL2;t=</sup> R0<sup>L2;t(i)di ,respectively.EachindividualoftheRicardianandHtM</sup> households can reset their nominal wage with constant probability 1 � �w in each period. Hence, the (nominal) wage decision of a HtM member i at time t = 0 is to choose W2<sup>�</sup> ;0<sup>(i)tomaximize</sup> (8) subject to (10) and other constraints, taking a lower adjusted discount factor �2 = �w� which incorporates the fact that W2<sup>�</sup> ;0<sup>(i)canberesetinthefuture.Theproblemisanalogousforthe</sup>

> 20 Giambatista and Pennings (2017) show in their Online Appendix 2.1 that when labor across Ricardian and HtM households are perfect substitutes and also coupled with the existence of a labor union, as in Galí et al (2007), the exact same allocations and multipliers are achieved as in the Cobb-Douglas speci...cation. See Giambatista and Pennings (2017) for further details of this equivalence.

> 21 Deviations of Ytf from Yt are second order in the neighborhood of the steady state, and so in the ...rst-order approximation we have Yt<sup>f=Yt.</sup>

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