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.
(a) On the graph below, 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.
(b) 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? x1 = 20, x2 = 10. How much of each input will the firm need to produce 20 juggernauts at the Inkster plant? x1 = 10, x2 = 20. 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.
(c) Label with a b on your graph the point that shows how much of each of the two inputs is needed in to 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 to 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 is oquant 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? Yes.