Please only do part b.

1. Consider a farmer with U(x, l) = axc - (1-1)2, where I represents leisure, xc represents a consump- tion good, and the individual has one unit of time that can be allocated to a combination of three possible uses: (1) leisure (1), (2) farm production (LF), (3) off-farm work (Ls). Farm production is characterized by Xp = ylog(L) where L is the total labor used on the farm and y > 0. Good x can be sold at price p or consumed directly, and the individual can also hire outside labor (LB) to work on the farm (such that L = LF + LB) or sell their own labor off of the farm (Ls) at wage rate w. You may assume interior solutions for this problem. (a) Derive the profit function and the cost function associated with the farm (and note the arguments associated with each function). Explain whether either function is homogeneous of a given degree in any or all of its arguments. Then, determine whether the farm production process exhibits decreasing returns to scale for at least some input levels. (b) Assuming the individual's objective is to maximize utility, write down the relevant maximization problem and solve for the utility-maximizing time use allocation and farm production level. Determine whether preferences are separable from farm production and (if Yes) the conditions under which they would continue to be separable if labor could not be sold off the farm. Be sure to justify your response