Question 5:

Letfbe a production function that exhibitsincreasingreturns to scale (IRS), andw1andw2be the market prices of inputs 1 and 2, respectively. Pick anyy >0 and anyt >1; let (x1,x2) be a cost-minimizing input bundle to produce the output quantityy. DenoteCfor the cost function, and AC for the average cost function. In the steps listed below, fill in the blanks with either a symbol among<, =,>,,, or the name of a theorem, or one of the items suggested in the parenthesis following the blank:

1. C(y)______w1x1+w2x2
2. f(tx1,tx2)________tf(x1,x2)_______ty
3. By the _________ theorem, withfdifferentiable andf(0,0) = 0, there exists anssuch thatf(sx1,sx2) =tyand ________ (0< s <1, 0< s < t, 0< t < s, 0< s).
4. C(ty)______w1sx1+w2sx2________w1tx1+w2tx2________tC(y), withsspecified in (c).
5. C(y)_______C(ty)/t
6. AC(y)_________AC(y) ify> y