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

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?

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a.We can let the price of good 2 be equa...

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