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A firm uses labor and capital as factors for a technology with constant returns to scale and strictly convex production function. A new manager, looking through past data, observed that:when factor prices were: wl = 20 and wk = 5; the firm hired l = 10 and k = 30 to produce outputy = 100;? when factor prices were: wl = 5 and wk = 12; the firm hired l = 18 and k = 36 to produce outputy = 150:
Assume that the past choices of labor and capital minimized costs given respective price levels.
a. Suppose that the current prices of factors are equal to wl = 5 and wk = 12: How much labor and capital should be hired if the new manager wants to produce output 300? How much if he wants to produce outoput 100? (Hint: Use the fact that the technology has a constant returns to scale).
Next, suppose that the current prices of factors change to wl = 10 and wk = 10 and the firm needs to hire labor and capital in order to produce y = 100 output: The deputy manager comes up with the following propositions:
b. l = 20; k = 10;c. l = 12; k = 30;d. l = 11; k = 23;e. l = 11; k = 28;f. l = 5; k = 100:
Which of the above propositions should be rejected by the manager?
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