(a) Suppose we have the following production function: Q=K2/3L2/3. Does the technology have constant returns to scale (CRS)? If not, what? Show your work and explain what it means. (b) What is the firm's cost minimization problem in the long-run? Explain and illustrate in a figure using isocost and isoquants how we determine optimal inputs K and L. (c) Now, consider the short-run where K is fixed at 8 (so that K2/3=4 ). Let r=$20 and w=$10. Show then discuss how short-run average costs change as Q rises. You can use math or a table/figure to do this. (d) Suppose P=$15. Show that optimal Q=64 in the short-run. You can use math or a spreadsheet. Show details. (e) Now suppose P=$5. Should the firm shut-down and set Q=0 ? Explain. (a) Suppose we have the following production function: Q=K2/3L2/3. Does the technology have constant returns to scale (CRS)? If not, what? Show your work and explain what it means. (b) What is the firm's cost minimization problem in the long-run? Explain and illustrate in a figure using isocost and isoquants how we determine optimal inputs K and L. (c) Now, consider the short-run where K is fixed at 8 (so that K2/3=4 ). Let r=$20 and w=$10. Show then discuss how short-run average costs change as Q rises. You can use math or a table/figure to do this. (d) Suppose P=$15. Show that optimal Q=64 in the short-run. You can use math or a spreadsheet. Show details. (e) Now suppose P=$5. Should the firm shut-down and set Q=0 ? Explain