Gudrun owns a factory that produces hats. For her production she needs labor (L) and capital (K). Her production function is q = 50L0.25K0.25. The hourly cost of capital is $1 and the hourly cost of labor is also $1. a) How much will her production increase if she doubles the inputs of both K and L? Does this function exhibit increasing, decreasing or constant returns to scale? b) What is the marginal rate of technical substitution (MRTS) for this production function (assume K is on the y-axis and L is on the x-axis)? Explain intuitively why the MRTS changes along the isoquant curve. c) Gudrun wants to produce 200 hats, find her optimal combination of K and L. What is the total cost of this production? d) Now Gudrun wants to immediately increase the production of hats from 200 to 400 hats. Explain how her production will change in the short run: How much K and how much L will she use in her production? What is the total cost of this production. e) Now explain what will happen in the long run if she wants to increase the production from 200 to 400 hats. How much K and how much L will she use in her production in the long run? What is the total cost of this production.