2015 EC 399 Midterm Exam complete solution correct answer key

2015 EC 399 Midterm Exam complete solution correct answer key

Jiabin Wu

Problem 1 (10 pts)

1) Suppose your budget is $5 dollars. The price for apples is always $1 each. The price for the _rst

banana is $2, and every subsequent banana costs $1. Draw your budget line.

Problem 2 (15 pts)

Suppose that Mr Smith is planning to hold a party on Saturday night. He needs some chips (in

bags) and sodas (in bottles). He is thinking about the following three combinations of chips and

sodas.

_ A = (3 chips; 2 sodas),

_ B = (1 chips; 4 sodas),

_ C = (5 chips; 1 sodas).

Assume that Mr Smith is rational and he is indi_erent between A and C, and he prefers C to B.

1) Suppose that the price for one bag of chips is $1 and the price for one bottle of soda is also $1

and Mr Smith has $5 in his pocket to spend on the party. What would Mr Smith choose among

the three combinations (Draw a graph to illustrate the 3 combinations and the budge line)? (6 pts)

Problem 3 (20pts)

Suppose that Kyle and Thomas are neighbors and they like to compare with each other (social

comparison). Suppose that Kyle is loss averse and his value function is given by v(x) = x=2 for

gains and v(x) = 2x for losses. In 2014, Kyle earned an income of $15k, while Thomas' income was

$12k. In 2015, Kyle's expected income is going to be $11k and Thomas's expected income is going

to be $15k.

Suppose Kyle uses the average expected income of himself and Thomas in year 2015 as his ref-

erence point. How much would he say that he lost in terms of value when his income dropped

from $15k to $11k from 2014 to 2015? Draw the value function for Kyle and identify the points

corresponding to his value of $15k and $11k.

Problem 4 (10pts)

Suppose you take three cards in a row from a well shu_ed deck of cards (52 cards in total). You

don't put the _rst card back in the deck before drawing the second card and you put the second

card back in the deck before drawing the third card.

1)      What is the probability of getting no Kings? (5 pts)

Problem 5 (20pts)

Peter know that Chris is a gentleman with _ne taste with probability 0.9 and he is not with proba-

bility 0.1. A person with _ne taste goes to a fancy restaurant on Friday night if he/she has a good

mood and goes to an ordinary restaurant on Friday night if he/she does not have a good mood.

Chris usually has a good mood on Friday night with probability 0.8. On the other hand, a normal

person eats at an ordinary restaurant regardless of his/her mood.

1) Suppose Peter sees that Chris is sitting in an ordinary restaurant having his dinner on Fri-

day night. What is the probability that Peter thinks that Chris is a normal person (use Bayes'

Rule)? (7 pts)

Problem 6 (25pts)

1) In the money payo_ matrix given in Table 1, which action would be favored by the minimax-

risk-criterion if a person's Bernoulli utility function is given by u(x) = x? As part of your answer,

draw the risk-payo_ matrix. (10 pts)