Consider the model of the representative firm studied in class. Recall that in this model, the firm lives for two periods, producing output in the first period, and output Y’ in the second period by operating the following technologies:
= z(K, ), ′ = z′H(K′)
where (K, K′) denotes physical capital in the first (second) period, is labour demanded in the first period, and z, z′ denotes total factor productivity in the first (second) period. The function is increasing in both arguments, it is concave, and it satisfies constant returns to scale. The function H is increasing and concave.
The firm hires labour in a competitive market at the wage . Capital in the first period K is fixed, and physical capital depreciates at the rate ∈ (0, 1) between periods, so that: K′ = (1 − )K + , where denotes investment.
The firm discounts future payoffs using the interest rate , and the objective of the firm is to maximise the present value of its profits.
a) Supposethatthankstomoderntechnology,thecapital depreciation rate decreases. What would be the effect on the firm’s investment decision?
b) Suppose that the government introduces a wage subsidy in the amount theta > 0 per unit of labour demanded by the firm. Write down the firm’s problem.
c) Whataretheeffectsofthissubsidytolabourdemand?Draw diagram that illustrate your answer.
d) Assuming that there is no subsidy and z = z′ = 1, = 0.02, = 0.05, = K0.30.7, H = (K′)0.5, K = 40
Compute the optimal level of investment of the firm ∗.