Consider the model of the representative firm studied in class. Flecall that in this model. the firm lives for two periods. producing output Y in the first period , and output Y' in the second period by operating the following technologies: v = zFfK, Nd), and Y\" = year\"), where K [K'] denotes physical capital in the first {second} period. Nd is labour demanded in the first period. and s (zit denotes total factor productivity in the first {second} period. The function F 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 to. Capital in the first period If is fixed, and physical capital depreciates at the rate a e {I}, 1} between periods, so that K' = {1 am + I, where I denotes investment. The firm discounts future payoffs using the interest rate 1", and the objective of the firm is to maximise the present value of its profits. (1} [9 marks] Suppose that the government introduces a wage subsidy in the amount a :r- [I per unit of labour demanded by the firm. Write down the optimisation problem of the representative firm, given the wage subsidy. (2} [9 marks] Using the optimisation problem of the firm, find the optimality condition which pins down the firm's labour demand. Provide an interpretation for such optimality condition. (3} [7 marks] Suppose that the wage subsidy e increases [all else equal). What is the effect on the labour demand? Provide an intuition based on the optimality condition derived in part (2}