1. [12 points, 3 points each] Assume that a certain company's productivity is modelled 5 by the Cobb-Douglas production function f(x, y) = 6xy, where x is the amount of money expended for labour and y is the cost of capital equipment. Assume that the company currently spends 21 units on capital equipment. (a) Find all x such that marginal productivity of labour equals the marginal produc- tivity of capital. (b) Find all x such that marginal productivity of labour is strictly less than the marginal productivity of capital. (c) Assume the company spends 7 units on labour. To increase productivity, should the company invest in capital expenditures or increase spending on labour? (d) Assume that over time, labour expenditure and capital investments are given by x(t) = 15+t, df dt' y(t) = 7+ t where t denoted time. Compute 14, using the multi variable chain rule, at t = 0, which is the production rate of change with respect to time at time zero.