Suppose a firm has a production function f(K, L) = K ^1 /6 L ^5 /6 .

1. Graph an isoquant.

2. what is the marginal product of capital and the marginal product of labor? Does it depend on how intensive the use of capital and labor are? Does the marginal product of a factor decrease with the quantity used?

3. What is the Marginal Rate of Technical Substitution for the production function provided? For all regions.

4. Given the price of capital (r = $12) and price of labor (w = $6), find the quantities of capital and labor that minimize the total cost, if the firm wishes to produce at least 240 units of output.

5. Determine (and provide a supporting argument to) whether the following claim is true or false: "The cost minimizing quantities of capital and labor equate the MRTS to the relative prices of inputs."

6. Write down the cost minimization problem for a firm with the production function given that wants to achieve an arbitrary level q of production. Solve for the factor demand 6 of capital and labor. Replace those quantities into the total cost function. Express the total cost function as a function of quantities produced.