Nadine sells user-friendly software. Her firm’s production function is f(x1, x2)

Question

Nadine sells user-friendly software. Her firm’s production function
is f(x1, x2) = x1 + 2x2, where x1 is the amount of unskilled labor
and x2 is the amount of skilled labor that she employs.

(e) If Nadine faces factor prices (1, 1), what is the cheapest way for her
to produce 20 units of output?

(f) If Nadine faces factor prices (1, 3), what is the cheapest way for her
to produce 20 units of output?

(g) If Nadine faces factor prices (w1, w2), what will be the minimal cost
of producing 20 units of output?

(h) If Nadine faces factor prices (w1, w2), what will be the minimal
cost of producing y units of output?

Please show specific process. Thanks.

Explanation / Answer

e) since MRTS = 0.5 < 1 = slope of iso-cost line

then, only use x2 = 20/2 = 10.

f) since MRTS = 0.5 > 0.33 = slope of iso-cost line

then, only use x1 = 20.

g) if MRTS = 0.5 < (w1/w2) = slope of iso-cost line then only x2 = y

  if MRTS = 0.5 < (w1/w2) = slope of iso-cost line then only x1 = y

Cost = min {w1,0.5w2}*20

h)  Cost = min {w1,0.5w2}*y

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