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Chapter23 - Chapter 23 Optimal Monetary Policy with Sticky...

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© Sanjay K. Chugh 287 Summer 2008 Chapter 23 Optimal Monetary Policy with Sticky Prices We now reconsider the issue of optimal monetary policy, this time in the Rotemberg sticky-price framework we just finished developing. We will find that the policy advice that arises in a sticky-price view of the economy is qualitatively quite different from the policy advice that arises in a flexible-price view of the economy. The work we do in this chapter builds on virtually all of the ideas and concepts we have laid out so far. We will rely on the Dixit-Stiglitz-Rotemberg model of price-setting firms subject to menu costs. Our mode of optimal-policy analysis will be identical to the structure by which we analyzed the optimal policy problem in Chapter 17. As there, we must first specify the private-sector equilibrium for any arbitrary policy the government (the central bank) might choose. This in itself requires setting up and solving the optimization problems of the demand and supply sides of the economy; we have already done most of this work, but there are a couple of new elements we introduce. Then, as in Chapter 17, in a second step, we determine the policy that maximizes the representative consumer’s utility. The final step is to compute the actual optimal policy, which is done by comparing the solution of the optimal policy problem with the outcome in the private-sector equilibrium; the result is the optimal policy recommendation. We once again – because, we continue to maintain, it seems very natural – adopt the representative consumer’s utility as the welfare criterion according to which the central bank ranks various policies. Thus, just as in our earlier analysis of optimal policy, we can think of the policy-makers as sitting “above” the economy, watching how equilibrium unfolds. We need to make a slight refinement to this view here, however: we will think of the policy-makers as watching how a symmetric equilibrium unfolds. Thus, policy-makers understand that for any given policy they choose, the private sector (consumers, retail firms, and wholesale firms) will make optimal choices that will result in some symmetric equilibrium. All of this by-now quite familiar machinery allows us to continue to think of the optimal policy problem as a problem of choosing the best equilibrium, where “best equilibrium” means the one that maximizes the utility of the representative consumer. Retail Firms The representative retail firm is again no different from the one we developed in the basic Dixit-Stiglitz and Rotemberg models: a retail firm simply “packages” the continuum [0,1] of differentiated wholesale products and sells the retail consumption basket to consumers via perfectly-competitive markets. As before, the price of retail goods is determined only through the invisible hand of the market, and the profit-maximizing choice of any arbitrary wholesale good j leads to the demand function for wholesale good j,
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© Sanjay K. Chugh 288 Summer 2008 1 jt jt t t P y y P H H ± § · ¨ ¸ © ¹ , (1.1)
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