7.1. A widget manufacturer has an infinitely substitutable production function of the form = 2K + L. a. Graph the isoquant maps for q = 20, q = 40, and q = 60. What is the RTS along these isoquants? b. If the wage rate (w) is $1 and the rental rate on capital (v) is $1, what cost-minimizing combination of K and L will the manufacturer employ for the three different production levels in part a? What is the manufacturer's expansion path? c. How would your answer to part b change if v rose to $3 with w remaining at $1?7.3. The long-run total cost function for a firm producing skateboards is TC = q - 30q + 350q, where q is the number of skateboards per week. a. What is the general shape of this total cost function? b. Calculate the average cost function for skateboards. What shape does the graph of this function have? At what level of skateboard output does average cost reach a minimum? What is the average cost at this level of output? c. The marginal cost function for skateboards is given by MC = 3q2 - 60q + 350. Show that this marginal cost curve intersects aver- age cost at its minimum value. d. Graph the average and marginal cost curves for skateboard production