Q1. Gary's labor supply is given by H = -10 + 0.71428.w, where H is the hours worked per week and w is the hourly wage rate. Mary and Terry's labor supply functions are represented by H= -2 + 0.25.w and H= -38+1.7272.w, respectively.
a) First, determine the reservation wage for each of these individuals, showing every step of your work. Please round to the second decimal point.
b) Second, if the market wage is $36, how many hours does each individual supply? And, at which wage rate would each individual supply 40 hours per week? Please round to the second decimal point.
c) Third, provide the market labor supply equation. Note that this is more difficult than it may initially seem, as the proper conditions need to be fully stated.
d) Lastly, in a separate figure, graph the market labor supply curve, labeling everything you can. Another quadrant may be used as needed for the intercept.
Q2) The Metal Company produces brass fittings for one cent a piece. Their production function is q = 500 . E^2 . K^3 , where q, E, and K are the numbers of fittings, workers, and machines, respectively. AMC's employees earn $15 an hour and machines are rented for $50 an hour, with $50,000 to spend on both inputs. With all of this given information, first calculate:
a) The short-run optimal amount of workers when only one machine is available.
b) The long-run optimal amounts of workers and machines. Now assume that MRTS is represented by a constant. For that case, recalculate:
c) The long-run optimal amounts of workers and machines.