Econ 313 - Wissink – Spring 2006
PS#4 - XtraQ
DUE: Wednesday March 15 in class
1. Suppose there is a 50-50 chance that a risk-averse individual with the utility function u=√($)
and with wealth of $20,000 will contract a debilitating disease and suffer a loss of $10,000.
a. What is the $expected value?
b. What is the expected utility of this probabilistic situation?
c. What is the $certainty equivalent?
d. What are the values of the $premium and $benefit of an insurance contract that leaves the
individual ex ante indifferent to buying the contract or taking the risk?
e. Suppose we increase the chances of getting the disease to .75. How will that change the
contract and the insuring firm’s expected profit?
2. Contrast the concepts of diminishing returns to scale and diminishing returns to a factor of
production. Can a production function exhibit diminishing returns to scale but NOT have
diminishing returns to a factor?
3. Suppose the production function for widgets is given by:
Q=KL - .8K2 - .2L2, where Q represents the annual quantity of widgets produced, K
represents annual capital input, and L represents annual labor input. Using this production
function, answer the following:
a. Suppose K=10. Graph the total and average product of labor curves. At what level of
labor input does this average product reach a maximum? How many widgets are
produced at that point?
b. Again assuming that K=10 and using the information that the MPL curve is a straight line
with an intercept of 10 (for L=0), graph this curve. At what level of labor input does
MPL=0?
c. Suppose capital inputs were increased to K=20, how would your answer to parts (a) and
(b) change?
4. Professor Smith and Professor Jones are going to produce a new intermediate
microeconomics textbook. As true scientists they have laid out the production function for
the book as: Q=S1/2J1/2, where Q=the number of pages in the finished book, S=the number of
working hours spent by Smith, and J=the number of hours spent working by Jones. Smith
values his labor at $3 per hour. He has spent 900 hours preparing the first draft. Jones,
whole labor is valued at $12 per hour, will revise Smith’s draft to complete the book.
a. How many hours will Jones have to spend to produce a finished book of 150 pages? Of
300 pages? Of 450 pages?
b. What is the marginal cost of the 150th page of the finished book? Of the 300th page? Of
the 450th page?