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Now switch to the firm perspective and suppose a firm produces output y with the Cobb-Douglas production function: y = 2????1 .5????

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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