Summary 221Study Hours Finance Grade Study Hours Economics Grade
07 00 7 5
17 81 8 1
28 32 8 5
38 83 8 7
49 04 8 9
59 25 9 0a. List the marginal values of additional hours worked for each subject.
b. How much time should the student spend studying each subject?
c. Suppose the student also is taking an accounting exam and estimates
that each hour of studying will raise her grade by three points. She has
allotted two hours for studying accounting (in addition to the five hours
already mentioned). Is this an optimal decision? Explain. (Assume her
objective is to maximize her average grade across the three courses.)
*14. Let Q L^ K^. Suppose the firm seeks to produce a given output while
minimizing its total input cost: TC PLL PKK. Show that the optimal
quantities of labor and capital satisfy L/K ( / )(PK/PL). Provide an
intuitive explanation for this result.
*15. In a particular region, there are two lakes rich in fish. The quantity of fish
caught in each lake depends on the number of persons who fish in each,
according to Q 1 10N 1 .1N 12 and Q 2 16N 2 .4N 22 , where N 1 and N 2
denote the number of fishers at each lake. In all, there are 40 fishers.
a. Suppose N 1 16 and N 2 24. At which lake is the average catch per
fisher greater? In light of this fact, how would you expect the fishers to
re-deploy themselves?
b. How many fishers will settle at each lake? (Hint: Find N 1 and N 2 such
that the average catch is equal between the lakes.)
c. The commissioner of fisheries seeks a division of fishers that will
maximize the total catch at the two lakes. Explain how he should use
information on the marginal catch at each lake to accomplish this
goal. What division of the 40 fishers would you recommend?Spreadsheet Problems
S1. A firm’s production function is well described by the equationInput prices are $10 per labor hour and $20 per machine hour, and the
firm sells its output at a fixed price of $10 per unit.Q2L.01L^2 3K.02K^2.
*Starred problems are more challenging.c05Production.qxd 9/5/11 5:49 PM Page 221