Now switch to the firm perspective and suppose a firm produces output y with the Cobb-Douglas production function: y = 2????1 .5????2 .5 .
a. Demonstrate the returns to scale of this technology.
b. If x2 is fixed at 1 unit, derive the marginal product of input 1.
c. If both the price of x1 (w1) and the output price (p) are equal to 1, how much of input 1 (x1) should the firm produce in the short run to maximize profits? (hint: use the profit maximizing "rule of thumb")
d. What is the profit maximizing firm's output level?
e. What are the firm's revenues? f. If w2 = 1, what are the firm's profits?
g. Should the firm shut down?
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