Here we consider firms producing with labour rather than capital. Assume there are two time periods t {0, 1}. A firm produces using production function yt = tn t where yt is output, t is productivity, nt is labour hours hired and (0, 1) is a parameter. The firm's objective is to maximise value for its risk neutral shareholders (who have discount factor [0, 1]). To hire nt units of labour, the firm must pay a wage bill of wtnt where wt is the wage rate per unit of labour. Note that the proceeds and costs of production at time t from hiring labour are realised and incurred respectively at time t. That is, in contrast to an inter-temporal decision as we had in class with capital investment, this firm makes purely intra-temporal decisions for each t. The firm's productivity t is non-random but potentially time-varying. The firm is subject to a corporate tax rate of (0, 1). 1. Assume that labour expenses are tax deductible. Write down this firm's optimisation problem and solution. Interpret. Find the value of the firm at the optimum. How do taxes affect the firm and its investors? Relate to the real world and interpret. 2. Now assume that labour expenses are not tax deductible. Re-do the steps in the previous section and compare to the tax deductible case. How would market clearing feature in the comparison? Relate to the real world and interpret