Question 4.

Let the production function be f(x1,x2) := 30x(1)^2/3 x(2)^1/2 for all nonnegative (x1,x2).

1. At any input bundle (x1, x2), the marginal product of input 1 is equal to________ , and the marginal product of input 2 is equal to_______
2. At the input bundle (x1,x2) = (2,3), the slope of the isoquant (level surface of the production function) at this bundle is equal to_______
3. Suppose that the price for input 1 is$10 and that for input 2 is$30, and that the firm needs to produce an output quantityyfor some parametery >0. Then...

i). the slope of the isoquant at the cost-minimizing input bundle is equal to ______-(the answer should be a real number)

ii). the cost-minimizing input bundle to produce output quantityyis to set

x1= _________andx2=__________ (the answers should be mathematical expressions ofy)

iii). the cost to produce output quantityyis equal to________ (the answer should be a mathematical expression ofy)

4. For anyt >1,f(tx1,tx2) =t^a f(x1,x2) wherea= ______ [the answer should be a real number], hencef(tx1,tx2)__________ (>,<, = [fill in the blank with one of the three items])tf(x1,x2) and thus the production function exhibits ___________ (constant,

increasing, decreasing [fill in the blank with one of the three items]) returns to scale