Suppose we have the following production function: Q = 4 K + 2 L. Confirm the technology is constant returns to scale (CRS). Show your work and explain what it means. (4 points) (b) Short-run: Suppose we had K = 10 fixed in the short-run but L is variable. Find the firm’s short- run cost function. Show that average costs fall as output rises. Explain why this happens. (4 points) (c) Suppose P = $7. Explain why the firm would want Q = 40 given r = $20 and w = $20 if K is fixed at 10. (4 points) (d) Long - run: now suppose K and L are both variable. Let r = $20 and w = $20. State the firm’s cost minimization problem. Show and explain using the isocost - isoquant figure. (2 points) (e) Find the firm’s long-run cost function. (4 points) (f) Suppose P = $7. Explain why the firm would want Q = infinity given r = $20 and w = $20 if both K and L variable