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北大光华管理学院周黎安老师中微习题答案
Answer to P.S. 2
1. Richard is deciding whether to buy a state lottery ticket. Each ticket costs $1, and the probability of
winning payoffs is given as follows:
Probability Return
0.5 $0.00
0.25 $1.00
0.2 $2.00
0.05 $7.50
a) What is the expected value of Richard’s payoff if he buys a lottery ticket? What is the variance?
b) Richard’s nickname is “No-risk Rick”. He is an extremely risk averse individual. Would he buy the
ticket?
Answer:
a) The expected payoff:
The variance:
b) No .
2. In class we showed the condition under which a risk neutral criminal will not commit crime.
Now suppose that this criminal is risk averse, can you still get conclusion that raising fine or raising
the probability of catching a violation will yield the similar deterrence effect? You may assume that
the criminal has an initial wealth or income W.
Answer:
Yes
His expected utility is :
E V 1=− p u W +R + pu(W −C) u i 0
( ) ( ) ( )
Then we have the first-order condition that
∂EV
=−u W +R +u(W −C) 0
( )
∂p
∂EV
=−pu (W −C ) 0
∂C
3. Suppose that the process of producing lightweight parkas by Polly’s Parkas is described by the
0.8 0.2
function Q = 10K (L-40) , where Q is the number of parkas produced, K is the number of machine
hours, and L is the number of person-hours of labors.
a) Derive the cost-minimizing demands for K and L as a function of Q, wage rates (w), and
rental rates on machines (r). Use these to derive the total cost function.
b) This process requires skilled
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