In: Economics
Problem 2. Consider the linear (perfect substitutes) production function f(x, y) = 12.7x + 19.4y.
(A) How many units of good y would be a perfect substitute for 1 unit of good x? What is the slope of the firm’s isoquants?
(B) Suppose the input prices are (px, py) = (5, 8). What is the slope of the isocost lines? How much output does the firm get when it inputs $1 worth of good x? How much output does the firm get when it inputs $1 worth of good y?
(C) Suppose this firm has a production quota of q = 500 units. Find the minimized cost C(500) and the corresponding conditional factor demands.
(D) Draw the firm’s level-500 isoquant, as well as the isocost lines. Indicate the cost minimizer on your diagram.