Since the economy is operating under perfect competition, the production function is linear homogeneous (constant returns to scale), and FN and FK depend only on KIN. The expressions for FN and FK can be linearized as follows (see the it 96 0), sPo s, time he Chapter 4: Anticipation Effects and Economic Policy Intermezzo below):

FN = [( 1 — COL) /OWN] k - =w, (4.29)

FK = (COL/aKN)[f< k], (4.30)

= ES [CV (4.31)

where FK dFK/FK, FN dFN/FN, dN/N, dK/K, dw/w, tL dta(1 - 0, NFN /17 Es g(N)/(NgN), and aKN FNFK /(YFNK). In words, a variable with a tilde represents the proportional rate of change in that variable, (Di, is the share of income paid out to the factor labour, Es is the labour supply elasticity (see Chapter 1)

that is assumed to be positive, and cJKN (> 0) is the substitution elasticity between capital and labour. Intuitively, it measures how easy it is to substitute one factor of production for the other. The easier the substitution, the higher the value for aKN.

Note that we have already imposed that the labour market is in equilibrium.

Intermezzo