a) Suppose we have the following production function: Q = min [10 K, L]. Confirm the technology is constant returns to scale (CRS). Show your work and explain what it means. (b) Show the isoquants in a figure. What are the input requirements for Q = 100? Explain how this tells you the input requirements for Q = 1. (c) Assume you are in the short-run with K = 10. Let r = $1000 and w = $10. Suppose the market price is P = $100. What is optimal output Q and optimal input L? Should the firm simply shut-down (Q = 0)? Why/why not. (d) What do we mean by a shut-down price? (e) Find the firm's shut-down price. That is, what is the minimum price that ensures the firm has positive output given r = $1000 and w = $10? Explain and show your work.