1. Returns to Scale Consider the following production function g = 21 + L% Does this production function have returns to scale? If so, which type? Show your proof. 2. Optimal Inputs Consider a rm that uses labor (L) and capital (K) to produce a general output (q) using the following production function: 1 3 q : Ki L1 The rm seeks to produce (1 = 100 units for sale and faces prices for labor of w = 2 and capital of "r : 6. a) What is the marginal rate of technical substitution? b) What are the optimal amounts of each input used by the rm? Round to three decimal places. c) How much does the rm spend? 3. Cost Functions Consider a rm that faces the total cost function TC : 500 + 4g + 6:12 where q is the output level of the rm. a) Is this a short run or long run cost function? How do you know this? b) Calculate the Average Fixed, Average Variable, and Average Total cost functions. c) Calculate the Marginal Cost Function