1. Consider a bond market in which only consumers borrow and lend. Assume that all 150

consumers have the same two-period consumption-utility function: U = c1c2. Let each of 100

consumers have the expected-income stream y1 = 10,000, y2 = 8400, and let each of the

remaining 50 consumers have the expected-income stream y1 = 8000, y2 = 14,000. At what

rate of interest will the bond market be in equilibrium?41

2. Consider an entrepreneur engaged in a point-input-point-output wine-aging process. His

initial cost is 20, the sales value of the wine is R(T) = 100, and the rate of interest is 0.05.

How long is his optimal investment period?

3. An entrepreneur is engaged in tree growing. He purchases a seedling for 4 dollars, incurs a

cultivation cost flow at a rate of G(t) = 0.4t dollars per year during the life of a tree, and sells

the tree at t = T for R(T) = 4 + 8T - T

2 dollars. The market rate of interest is 0.20. Determine

an optimal length for his cultivation period, T. Apply the appropriate second-order condition

to verify that your solution is a maximum.

4. An entrepreneur plans for a one-machine horizon. He purchases the machine for 500 dollars.

Its scrap value at time T is S(T) = 500 - 40T. The rate of interest is 0.05. The machine yields

a quasi-rent flow at the rate Zt = 85 - 4t dollars per year. When should the entrepreneur

retire this machine?

5. Ann, Ben, Can, and Den think of one natural number. Ann says it consists of two digits. Ben

says it is a divisor of 150. Can says it is not 150. Den says it is divisible by 25. Which one of

them is not telling the truth?

6. A painting job can be completed by 7 painters in 41 days. If 21 more painters join the team 9

days after starting work on the job, then how many more days are required to complete the

job?

7. Three coworkers would like to know their average salary. However, they are self-conscious

and don't want to tell each other their own salaries, for fear of either being ridiculed or getting

their houses robbed. How can they find their average salary, without disclosing their own

salaries?

8. Clark, Daw and Fuller make their living as carpenter, painter and plumber, though not

necessarily respectively. The painter recently tried to get the carpenter to do some work for

him, but was told that the carpenter was out doing some remodelling for the plumber. The

plumber makes more money than the painter. Daw makes more money than Clark. Fuller

had never heard of Daw. What is each man's occupation?

9. The sales tax you pay while purchasing a toothpaste is

(a) Tax imposed by Central Government

(b) Tax imposed by Central Government but collected by the State Government

(c) Tax imposed by State Government but collected by the Central Government

(d) Tax imposed and collected by the Central Government

10. What does "Venture Capital" mean?