Consider a firm that operates with the following production function: q=2KL²

a. Calculate the marginal products of labor and capital (MP_L and MP_K)

b. Calculate the marginal rate of technical substitution of labor for capital, MRTS_LK Firm faces markets for labor and capital, with rental rate r=1 and wage w=1

c. Consider a cost-minimizing input choice (in the long-run) - what would be the optimal K/L ratio?

d. Write down total cost of the firm (using given r and w) - isocost equation (function of K and L)

e. Use your results in c and d to find:

total cost function as a function of K only

production function as a function of K only

f. Use your results in e and write down cost function of the firm as C(q) <- no L or K, only q