Question

# 1. A ﬁrm has two variable factors of production, and its production function is f(x1,x2) =...

1. A ﬁrm has two variable factors of production, and its production function is f(x1,x2) = x1/2 1 x1/4 2 . The price of the output is 6. Factor 1 receives the wage \$2, and factor 2 receives the wage \$2. a. How many units of each factor will the ﬁrm demand? b. How much output will it produce?

2. Beth produces software. Her production function is f(x1,x2) = 3x1 + 2x2, where x1 is the amount of unskilled labor and x2 is the amount of skilled labor she employs. (a) Draw the isoquants representing combinations of inputs needed to produce 30 units, and 60 units. (b) Does the production function exhibit increasing, decreasing or constant returns to scale? (c) If Beth faces factors prices (2, 1), what is the cheapest way for her to produce 30 units of output?

1.

using standard marshellian condition

mpl/mpk = pk/pl

1/2x-1/2 .x21/4 / . 1/4x2-3/4 . x11/2 = 2/2

2x2/ x1 =1

2x2 = x1

f= 2x21/2 * x21/4 = 2x23/4

2.

30 = 3x1+2x2

x1 = 0 , x2 = 15

x2= 0 , x1 =10

60 = 3x1+2x2

x1= 0 , x2 = 30

x2= 0 , x1 = 20

b) Constant returns to scale

c) since the production function is subsitutes

x1 = 0 (cost of producting is higher than cost of producing x2)

x2 = output/price = 30/1 = 30

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