Short-Run Equilibrium

Abstract

At first have a look at the goods market. Firms produce as much as households, firms and the government want to buy Y = C + I + G, hence the goods market clears. In doing this, firms employ capital K and labour N. For ease of exposition, let technology be of the Cobb-Douglas type Y = K^α N^β with α > 0, β > 0 and α + β = 1. Firms maximize profits Π = pY − rpK − wN under perfect competition. From this follows r = ∂Y/∂K = αY/K. As a consequence, the interest rate accords with the marginal product of capital. This in turn yields the desired stock of capital K* = αY/r. Likewise one obtains w/p = ∂Y/∂N = βY/N. That means, real wages harmonize with the marginal product of labour.