Exchange Rates and Labor Demand: Profit maximizing producers sell to both domestic and foreign markets and are faced with a variety of demand shocks. Producer decisions depend on the future paths of all variables influencing profitability. In our context, the unknowns to the producer are aggregate demand in domestic and foreign markets, denoted y and y *, and the exchange rate, e, is defined as domestic currency per unit of foreign exchange. Production uses three factors: domestic labor L, domestic capital and other domestic inputs Z, and imported productive inputs, Z*. Respective factor prices are denoted by w, s, and es*. Our focus in the paper is on one factor input, domestic labor. We model changes in the use of domestic input subject to a partial adjustment cost. For simplicity, we assume that labor is a homogeneous input into production and that the levels of capital and foreign inputs can be fully adjusted in the short run with no additional costs this.
Within an industry, the representative producer chooses factor inputs and total output in order to maximize the expected present value of the flow of current and future profits, P, (equation 1). The optimization is subject to the constraints posed by its production structure additional costs involved in changing its level of domestic labor (equation 4). Profits are garnered from the sales in the home market, q, and the sales in the foreign market, q*. In addition, home and foreign sales depend on aggregate demand conditions in the respective markets, i.e. on y and y *
The time discount factor is defined by ft = U8T. In equations (2) and (3) we have dropped the period t time subscripts for convenience. . In equation (2), a Cobb-Douglas production structure is assumed for simplicity, but our main results also will hold under a more general CES production structure.
In equation (3) the parameters h and h* are, respectively, the domestic and foreign product demand elasticities facing producers in their own industries. The demand curves in domestic and foreign markets include multiplicative demand shifters, a(y,e) and a * (y*, e), which allow for independent roles of local market real income and of exchange rates. Exchange rates influence demand by potentially leading to shifts in the relative price of home products versus those of foreign competitors,10 and therefore, affecting the residual demand faced by the domestic firm .
In equation (4) the costs of adjusting an industry’s labor input, assumed to be quadratic, are fixed per worker in wage units, reflecting labor force adjustment costs that rise in proportion to wages. The parameter b reflects the costs of adjustment of the level of labor and should be viewed as being industry specific. The use of a quadratic formulation for adjustment costs is standard in the literature and should not be as an attempt to closely represent reality since it implies that firing and hiring costs are identical. However, it should be interpreted as a convenient simplification since it allows a straightforward empirical implementation of the labor demand equation.
The solution to the firm’s optimal labor demand problem is a dynamic equation. This equation is derived from the first-order conditions in each factor, and equates the marginal revenue product from an additional unit of labor today to the marginal cost of that unit for the firm.