Assignment:
1. Currently
MPs/Ps > MPa/Pa
where "s" and "a" refer to steel and aluminum, and Ps and Pa refer to the prices of steel and aluminum, and MPs and MPa refer to the marginal products of steel and aluminum, respectively, for a firm. Has the firm come up with the right amounts of steel and aluminum, or should it reallocate its resources to make the maximum profit?
2. The Springfield Bank received 1,500 inquiries following its latest advertisement describing its "establish a Certificate of Deposit (CD)-get a free CD (compact disk)" promotion in the Springfield Shopper, a local newspaper. The most recent similar ad in a similar advertising campaign was in the Brockman Business Newsletter. A local business publication generated 500 inquiries. Each ad in the Springfield Shopper costs $500. Each ad in the Brockman Business Newsletter costs $125. Inquiries from both publications have the same success rate in turning inquiries into sales.
(a) Assuming that additional ads will generate similar response rates, is Springfield Bank running an optimal mix of ads in the Springfield Shopper and the Brockman Business Newsletter? Why or why not?
(b) If you claim that the Springfield Bank is currently running an optimal mix of ads, clearly explain why they are using an optimal mix of ads. If you claim that the Springfield Bank is currently not running an optimal mix of ads, clearly explain how the Springfield Bank can better manage the ads.
3. Always Round Tire has a production function of Q = 300 L.75 K.5. In the short run, if L = 250 and K = 25, what is the quantity of tires supplied? What happens to the output of tires if L jumps to 300 and then 350? What law does this illustrate?
4. Currently,
MPs = 0.5Q/s and MPa = 0.5Q/a
where MPs and MPa are the marginal products of steel and aluminum for a company whose production function is Q = s0.5 a0.5. Ps = Pa = $1 are the prices of steel and aluminum, respectively, and the company has a total budget of $2 to spend on these inputs. If the market price of the output is $3 per unit, then how many units of s and a should the firm hire? What will be its output, revenue, costs, and profits?