The firm employs workers (L) and capital (K) according to the following production function:

q = L²K,

where q is the number of units produced, the hourly rental cost of capital (r) is $20 and the hourly cost of workers (w) is $10.

a) What is the marginal product of labor (MPL)? (1 point)

b) What is the marginal product of labor (MPK)? (1point)

c) What is the firm's MRTS? (1point)

d) Are there increasing, decreasing, or constant returns to scale? What does this mean? Show the proof. (2 points)

e) What is the firm's SRTC and SRAVC functions, if capital is fixed such that = 5? (2 points)

f) How much would it cost for Stephanie to produce 1000 cases of beer in the short-run if = 5? (1 point)

g) Derive the LRTC of the firm for any level of q. (2 points)