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9.2Pricing to Market

The integration of international commodity markets in the Redux model rules out deviations from the law-of-one price in equilibrium. Were such violations to occur, they presumably would induce consumers to take advantage of international price di erences by crossing the border to buy the goods (or contracting with foreign consumers to do the shopping for them) in the lower price country resulting in the international price di erences being bid away.

We will now modify the Redux model by assuming that domestic and foreign goods markets are segmented. Domestic (foreign) agents are unable to buy the domestically-produced good in the foreign (home) country. The monopolistically competitive Þrm has the ability to engage in price discrimination by setting a dollar price for domestic sales that di ers from the price it sets for exports. This is called pricing-to- market.

For concreteness, let the home country be the ‘US’ and the foreign country be ‘Europe.’ We assume that all domestic Þrms have the ability to price-to-market as do all foreign Þrms. This is called ‘full’ pricing- to-market. Betts and Devereux [10] allow the degree of pricing-to- market–the fraction of Þrms that operate in internationally segmented markets–to vary from 0 to 1. Both the Redux model and the next model that we study are nested within their framework. The associated notation is summarized in Table 9.2.

Full Pricing-To-Market

We modify Redux in two ways. The Þrst di erence lies in the pricesetting opportunities for monopolistically competitive Þrms. The goods market is integrated within the home country and within the foreign country, but not internationally. The second modiÞcation is in the menu of assets available to agents. Here, the internationally traded asset is a nominal bond denominated in ‘dollars.’ The model is still set in a deterministic environment.

Goods markets. A US Þrm z, sells xt(z) units of output in the home market and exports vt(z) to the foreign country. Total output of the

288CHAPTER 9. THE NEW INTERNATIONAL MACROECONOMICS

price of the bond is

1

δt ≡ (1 + it).

The foreign nominal interest rate is given by uncovered interest parity

à !

(1 + it ) = (1 + it) SSt .

t+1

Households. We need to distinguish between hours worked, which is chosen by the household, and output which is chosen by the Þrm. The utility function is similar to (9.2) in the Redux model except that

(181) hours of work ht(z) appears explicitly in place of output yt(z)

The associated price indices for the domestic and foreign households are

Wt is the home country competitive nominal wage. The household derives income from selling labor to Þrm z, Wtht(z). Household-z also owns Þrm-z from which it earns proÞts, πt(z). Nominal wealth taken into the next period consists of cash balances and bonds (Mt + δtBt). This wealth is the result of wealth brought into the current period (Mt−1 + Bt−1) plus current income (Wtht(z) + πt(z)) less consumption and taxes (PtCt + PtTt). The home and foreign budget constraints are given by

Households take prices and Þrm proÞts as given and choose Bt, Mt, and ht. To derive the Euler-equations implied by domestic household

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Foreign household demand for domestic z-goods and for and foreign z -goods are

Firms. Firms only employ labor. There is no capital in the model. The domestic and foreign production technologies are identical and are linear in hours of work

yt(z) = ht(z), yt (z) = ht (z).

The domestic z-Þrm sets prices at the beginning of the period before period-t shocks are revealed. The monopolistically competitive Þrm maximizes proÞts by choosing output to set marginal revenue equal to marginal cost. Given the demand functions (9.118)—(9.121), the rule for setting the price of home sales is the constant markup of price over costs,10 pt(z) = [θ/(θ − 1)]Wt. The z-Þrm also sets the euro price of its exports qt (z). Before period t monetary or Þscal shocks are revealed, the Þrm observes the exchange rate St, and sets the euro price according to the law-of-one price Stqt (z) = pt(z). This is optimal, conditional on the information available at the time prices are set because home and

spect to y yields marginal revenue, [(θ − 1)/θ]PC1/θy−1/θ = [(θ − 1)/θ]p. Marginal cost is simply W . Equating marginal cost to marginal revenue gives the markup rule.

foreign market elasticity of demand is identical. Although the Þrm has the power to set di erent prices for the foreign and home markets it chooses not to do so. Once pt(z) and qt (z) are set, they are Þxed for the remainder of the period. The foreign Þrm sets price according to a similar technology.

Output is demand determined in the short run and can either be sold to the domestic market or made available for export. The adding-up constraint on output, sales to the home market and sales to the foreign market are

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Government. Government spending is Þnanced by tax receipts and seignorage

In characterizing the equilibrium, it will help to consolidate the individual’s and government’s budget constraints. Substitute proÞts (9.122)- (9.123) and the government budget constraints (9.134)-(9.135) into the household budget constraints (9.110)-(9.111) and use the zero-net supply constraint Bt = −(n/(1 − n))Bt from (9.137) to get

(9.137) The equilibrium is characterized by the Euler equations (9.112)—(9.117), the consolidated budget constraints (9.136) and (9.137) with B0 = G0 = G0 = 0, and the output equations (9.128)—(9.133).

From this point on we will consider only on monetary shocks. To simplify the algebra, set Gt = Gt = 0 for all t. We employ the same solution technique as we used in the Redux model. First, solve for the 0-steady state with zero-international debt and zero-government spending, then take a log-linear approximation around that benchmark steady state.

The 0-steady state. The 0-steady state under pricing-to-market is identical to that in the redux model. Set G0 = G0 = B0 = 0. Dollar (189) prices of z and z goods sold at home are identical, p0(z) = q0(z ). From the markup rules (9.124) and (9.125), it follows that the law of one price, p0(z) = q0(z ) = S0q0(z) = S0p0(z ). We also have by PPP

Log-linearizing the labor supply rules (9.116) and (9.117) and using the price markup rules (9.124)—(9.125) to eliminate the wage yields

Log-linearizing the intertemporal Euler equations (9.112) and (9.113) gives

Long-Run Response

The log-linearized equations hold for arbitrary t and also hold in the new steady state. By the intertemporal optimality condition (9.112),

ˆ

δ = β in the new steady state which implies δ = 0. Noting that the nominal exchange rate is constant in the new steady state, it follows from (9.141) and (9.142)

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