Suppose we live in an exchange economy with two goods.I own 50 of both goods,and you own 250 of both goods.My tastes are captured by the utility function $$u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 50 \ln x _ { 1 }$$ and yours are captured by the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 100 \ln x _ { 1 }$ .
a.Calculate the competitive equilibrium price.
b.How much do each of us consume of good 1 in equilibrium?
c.Suppose the government transfers 100 units of your good 1 endowment to me.How is your answer to (a)and (b)affected?
d.Suppose the government instead transfers 100 units of good 2 from you to me.How is your answer to (a)and (b)affected?
e.Do you think your answers to (c)and (d)generally hold for most types of tastes -- or do you think they arise because of some specific feature of these tastes?

Question

Suppose we live in an exchange economy with two goods.I own 50 of both goods,and you own 250 of both goods.My tastes are captured by the utility function $$u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 50 \ln x _ { 1 }$$ and yours are captured by the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 100 \ln x _ { 1 }$ . 
a.Calculate the competitive equilibrium price.
b.How much do each of us consume of good 1 in equilibrium?
c.Suppose the government transfers 100 units of your good 1 endowment to me.How is your answer to (a)and (b)affected?
d.Suppose the government instead transfers 100 units of good 2 from you to me.How is your answer to (a)and (b)affected?
e.Do you think your answers to (c)and (d)generally hold for most types of tastes -- or do you think they arise because of some specific feature of these tastes?

Quizplus · Accepted Answer

The Answer of Suppose we live in an exchange economy with two goods.I own 50 of both goods,and you own 250 of both goods.My tastes are captured by the utility function $$u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 50 \ln x _ { 1 }$$ and yours are captured by the utility function $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 100 \ln x _ { 1 }$ . 
a.Calculate the competitive equilibrium price.
b.How much do each of us consume of good 1 in equilibrium?
c.Suppose the government transfers 100 units of your good 1 endowment to me.How is your answer to (a)and (b)affected?
d.Suppose the government instead transfers 100 units of good 2 from you to me.How is your answer to (a)and (b)affected?
e.Do you think your answers to (c)and (d)generally hold for most types of tastes -- or do you think they arise because of some specific feature of these tastes?

Suppose We Live in an Exchange Economy with Two Goods u(x1,x2)=x2+50ln⁡x1u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 50 \ln x _ { 1 }u(x1​,x2​)=x2​+50lnx1​

Suppose We Live in an Exchange Economy with Two Goods $u \left( x _ { 1 } , x _ { 2 } \right) = x _ { 2 } + 50 \ln x _ { 1 }$