# Homework 2 Solving for Equilibrium

Homework 2 Solving for Equilibrium 150 150 Affordable Capstone Projects Written from Scratch

Homework 2 Solving for Equilibrium
• All answers must be typed in WORD.
• Use “Alt” + “+” for typing equations in WORD.
• Discussions of homework with classmates are highly encouraged. However, after
discussions, everyone is responsible for writing and turning in their own homework.
1. (10’) Most countries in the world are fighting inflation, while Japan is struggling to
create inflation. Intuitively, why is deflation bad for Japan?
2. (10’) Why is barter less efficient than an economy with money? Give an example
(different from the one discussed in class).
3. (20’) Tom is 45 years old, working as a shark farmer in half moon bay. He will work for
another 20 years, then retire at 65, live another 20 years, then die at 85. Tom catches 1
shark every year before retirement. Total income before retirement is 20 sharks. Tom
likes eating sharks now, as well as after retirement. He has utility ln (c1) + ln (c2).
However, sharks CANNOT be stored for 20 years w/o going bad. One thing Tom can
do is to sell sharks in the market for \$100 each today. Then he saves the money in a
bank, which offers 0 interest. After retirement, Tom cash out his saving, use it to buy
sharks back. In 20 years, due to inflation, price of sharks will go up to \$200 per shark.
If you were Tom, what will you do to maximize your lifetime happiness?
4. (20’) You have an avocado tree, which grows 150 avocados this year, 50 next year.
Both you and your neighbor has utility function ln (c1) + ln (c2).
(a) (10’) Under agreement “1 today = 1 tomo”. How many do you want to lend?
How many does your neighbor want to borrow? Is this an equilibrium outcome?
(b) (10’) What is the condition satisfied by equilibrium outcome? Solve for equilibrium
exchange rate. What do you and your neighbor end up consuming under
this agreement?
5. (20’) You have 10 apples and 20 bananas. Your neighbor has 5 apples and 2 bananas.
Both you and your neighbor enjoy consuming apples and bananas and have utility
function ln (c1) + ln (c2), where c1 is the number of apples consumed and c2 is the
number of bananas consumed.
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(a) (10’) Under agreement “1 apple = 2 banana”. How many apples do you want to
purchase? How many apples does your neighbor want to trade away? Is this an
equilibrium outcome?
(b) (10’) What is equilibrium condition? Solve for equilibrium exchange rate. What
do you and your neighbor end up consuming under this agreement?
6. (20’) In a hunter-gatherer society lives 2 people, Adam and Smith. Adam is a hunter
and he catches 10 bears a week. Smith is a gatherer and he gathers 20 gigantic wildberries
a week. Both Adam and Smith enjoy eating bears and wild-berries and have
utility function ln (c1) + ln (c2).
(a) (10’) Under agreement “2 bear = 1 berry”. How many bears does Adam want to
sell? How many bears does Smith want to buy? Is this an equilibrium outcome?
(b) (10’) What is equilibrium condition? Solve for equilibrium exchange rate. What
do Adam and Smith end up consuming under this agreement?
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