Question

General Monsters Corporation has two plants for producing juggernauts, one in Flint and one in Inkster. The Flint plant produces according to fF (x1, x2) = min{x1, 2x2} and the Inkster plant produces according to fI (x1, x2) = min{2x1, x2}, where x1 and x2 are the inputs. 1. On a graph, use blue ink to draw the isoquant for 40 juggernauts at the Flint plant. Use red ink to draw the isoquant for producing 40 juggernauts at the Inkster plant. 2. Suppose that the firm wishes to produce 20 juggernauts at each plant. How much of each input will the firm need to produce 20 juggernauts at the Flint plant? How much of each input will the firm need to produce 20 juggernauts at the Inkster plant? Label with an a on the graph, the point representing the total amount of each of the two inputs that the firm needs to produce a total of 40 juggernauts, 20 at the Flint plant and 20 at the Inkster plant. 3. Label with a b on your graph the point that shows how much of each of the two inputs is needed in total if the firm is to produce 10 juggernauts in the Flint plant and 30 juggernauts in the Inkster plant. Label with a c the point that shows how much of each of the two inputs that the firm needs in total if it is to produce 30 juggernauts in the Flint plant and 10 juggernauts in the Inkster plant. Use a black pen to draw the firm’s isoquant for producing 40 units of output if it can split production in any manner between the two plants. Is the technology available to this firm convex?

Answer 1

fF = Min { X1, 2X2 }

At eqm, X1 = 2X2

X2 = .5X1

IC are Right angled shape , with kink along line, X2= .5X1

for Q = 40, X1 = 40, X2 = 20

.

fI = Min { 2X1, X2 }

At eqm, 2X1 = X2,

Again right angled IC

For Q = 40, X1 = 20 & X2 = 40

.

B) for 20 units

At plant F, X1 = 2X2 = 20

X1 = 20, X2 = 10

.

at plant I, 2X1 = X2 = 20

X1 = 10, X2 = 20

.

3) new points

At QF = 10

Then X1 = 10, X2 = 5

& QI = 30

X1 = 15, X2 = 30

4) yes, technology is Convex