Question: Just need help with C and D, I believe A us 102.5million widgets and B is 102.76 million. Thank you Problem: Suppose that the annual
Problem: Suppose that the annual output of the Acme Co. widget factory can be modeled by the production function Q=3K0.67L0.33 where Q is the number of millions of widgets produced, K is physical capital measured in millions of dollars, and L is labor measured in thousands of person-hours. This means that if the factory has a workforce of 50 employees working an average of 2,000 hours per year, the contribution of labor is measured as L=502 thousand person-hours. A. [2 points] If Acme has a work force of 50 employees that work 2,000 hours per year and invests 20 million dollars in the factory, approximately many widgets are produced? The exponents of K and L, called the elasticity of output, measure the responsiveness to the output when a change is made to capital or labor, respectively. Here they are approximately 2/3 and 1/3. B. [4 points] The CEO of Acme Co. is convinced that because the relative contribution of capital is double that of labor, the same level of production can be attained through increased capital investments (equipment upgrades and increased automation) with a much reduced workforce. Is the CEO correct? If the current capital is doubled and labor is reduced to a quarter of the original, how does the output compare to the answer to Part A.? C. [ 5 points] A single example (like Part B) may be convincing, but you now have, with the help of Section 14.2, enough mathematical skill to better answer this question. For the greatest increase in productivity, should the CEO of Acme Co of the company increase the use of labor or increase use of capital? Explain. (Assume the same values as Part A) D. [4 points] The Beta Company also produces widgets. Market analysis finds that the number of Acme widgets sold depends of the price p of Acme and the price q of Beta widgets: Acme: a=f(p,q)=5000.5pq2 Similar the number of Beta widgets sold can be described by Beta: b=g(p,q)=100008p100q2 Are the widgets made from Acme Co. and Beta Co. complementary or competitive products? Explain
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