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Problem 3. Consider the Leontiev (perfect complements) production function f(x, y) = M in x 9.6...

Problem 3. Consider the Leontiev (perfect complements) production function f(x, y) = M in x 9.6 , y 5.2 .

(A) How many units of good y would be a perfect complement for 1 unit of good x? What is the equation of the firm’s kink line?

(B) Assume the firm has a production quota of q = 400 units. Graph the firm’s level-400 isoquant. What are the coordinates of the kink?

(C) Suppose the input prices are (px, py) = (16, 9). Find the minimized cost C(400). What is the cost-minimizing input bundle (x ∗ , y∗ )?

(D) Give a complete geometric illustration of this firm’s cost minimization. On a single diagram, draw the firm’s level-400 isoquant, the isocost lines, and the cost-minimizing input bundle

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