Consider two agents, Adam and Smith, and two goods: wheat (w); milk (m). Adam has utility...

 

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Consider two agents, Adam and Smith, and two goods: wheat (w); milk (m). Adam has utility uA(w, m.) = 2w^1/4m^1/4 over the consumption of a quantity w of wheat and a quantity m of milk. Smith has utility us(w, m.) = w^1/3 m^2/3. Adam and Smith are both endowed with a quantity r of wheat and a quantity 2 of milk, where I> 0. 1. What is their initial utility? 2. Would they be willing to trade between each other and barter some milk for some wheat? If so, in which direction would such barter take place, and why? 3. A famous Scottish economist argues that barter is inefficient as it requires a double coincidence of wants, and that it justifies the use of money I If we were to intro- duce money to Adam and Smith, which "price" of wheat relative to milk would be acceptable and foster an exchange? Consider two agents, Adam and Smith, and two goods: wheat (w); milk (m). Adam has utility uA(w, m.) = 2w^1/4m^1/4 over the consumption of a quantity w of wheat and a quantity m of milk. Smith has utility us(w, m.) = w^1/3 m^2/3. Adam and Smith are both endowed with a quantity r of wheat and a quantity 2 of milk, where I> 0. 1. What is their initial utility? 2. Would they be willing to trade between each other and barter some milk for some wheat? If so, in which direction would such barter take place, and why? 3. A famous Scottish economist argues that barter is inefficient as it requires a double coincidence of wants, and that it justifies the use of money I If we were to intro- duce money to Adam and Smith, which "price" of wheat relative to milk would be acceptable and foster an exchange?

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