Aperfectly competitive firm produces output q with capital k and labor l according to the production function:

q = f(k, l) = 4k^1/4 l^ 1/4

the price of labor is w = 4, and the price of capital is r = 4. the firm has fixed costs equal to 8. the current market price is 8.

(a) prove that this production function has decreasing returns to scale.

(b) find the optimal (cost-minimizing) ratio of capital to labor inputs k/l for any level of output (use scale expansion path).

(c) for any q, and the cost minimizing inputs as functions of output: i. e., derive functions l(q) and k(q).

(d) find cost functions tc(q), atc(q), and mc(q), i. e. as functions of output. at what value of q does the minimum of atc occur?

(e) find total and marginal revenue as functions of output, i. e. tr(q) and mr(q). (f) find the pro t maximizing output q∗ and use that to and tr(q*), tc(q*), π(q*), l(q*), and k(q*).

(g) will other rms have an incentive to enter or exit this market? what will be the new market price that results from the entry/exit of firms? at the new price, what is the rm's new output? what is the rm's profit?

Anderson, a computer engineer, and spouse, who is unemployed, provide more than half of the support for their child, age 23, who is a full-time student and who earns $7,000. they also provide more than half of the support for their older child, age 33, who earns $2,000 during the year. how many dependents may the andersons claim on their joint tax return?

Insurance companies have internal controls in place to protect assets, monitor the accuracy of accounting records and encourage operational efficiencies and adherence to policies. these internal controls are generally of two types: administrative controls and accounting controls. administrative controls are the policies and procedures that guide the daily actions of employees. accounting controls are the policies and procedures that delineate authorizations of financial transactions that are done, safeguard assets, and provide reports on the company’s financial status in a reliable and timely manner. internal controls should include both preventative and detective controls. the purpose of preventative controls is to stop problems and errors before they occur. detective controls identify problems after they have occurred. preventative controls are usually more effective at reducing problems, but they also tend to be more expensive. internal controls must be flexible to adjust for changes in laws and regulations in addition to adding new products or modifying current ones. companies must also do regular analyses to ensure that the benefits of implementing the controls are worth their costs. when concerned about paying unwarranted insurance claims which type of control would be useful?

Suppose your rich uncle gave you $50,000, which you plan to use for graduate school. you will make the investment now, you expect to earn an annual return of 6%, and you will make 4 equal annual withdrawals, beginning 1 year from today. under these conditions, how large would each withdrawal be so there would be no funds remaining in the account after the 4th withdraw?