Question 5. (20) Consider a farm, which produces food using labour L and machinery M, according to the following function. F = aM Ll- where BE (0, 1) (a) (10 points) Calculate and interpret the following partial derivatives al and OF BI; as well as the cross-partial O'F Mraz: Interpret the parameters a and 8 in this model. (b) (10 points) Assume the cost of investing in new machinery is very high, so that in the short-run we can view M as fixed. Assume that workers are plentiful and the farm can hire as many as they want at a cost (wage rate) w. Furthermore, the farm sells food at a constant price p. i. Set up short-run profit as a function of L and solve for the optimal choice of L. ii. How does the optimal choice of L depend on the fixed level of MY Explain