Question

# 2. Consider an economy with two goods, x and y with prices px and py, respectively....

2. Consider an economy with two goods, x and y with prices px and py, respectively. We observe the following choices made by Rob: if px > py he chooses to consume only y, and if py > px he chooses to consume only x. Suggest a utility function for Rob that represents preferences consistent with the given data. (5m)

3. Consider a market for used cars. There are many sellers and even more buyers. A seller values a high quality car at 800 and a low quality car at 200. For any quality, the value to buyers is m times the value to sellers, where m > 1. All agents are risk-neutral. Sellers know the quality of their own car, but buyers only know that 2/3 of the cars are low quality and the remaining 1/3 of them are high quality. For what values of m do all sellers sell their used cars? 4. If the price elasticity of supply is zero, a tax on suppliers will raise the market price. Is this true or false? Explain your answer. (5m)

4. If the price elasticity of supply is zero, a tax on suppliers will raise the market price. Is this true or false? Explain your answer. (5m)

6. An individual consumes two goods and her preferences satisfy non-satiation. It follows that at least one of the two goods must be a normal good. Is this true or false? Explain your answer. (5m)

7. Under first-degree price discrimination, a monopolist produces the efficient output. Is this true or false? Explain using an appropriate diagram. 8. Several generators pollute the environment by emitting carbon dioxide. Generators have different costs of reducing carbon emissions. The government wants to put a cap on total emissions. Putting a cap on each generator is more efficient compared to issuing tradeable emissions permits to each generator. Is this true or false? Explain your answer. (5m)

2. We are given the choices made by rob. He only consumes good X when the price of good X that is Px is less than the price of good Y that is Py. And when the price of good Y that is Py is less than the price of good X that is Px, he only consumes good Y.

With the given information we can infer one thing about rob's choices that he doesn't care about what good is he consuming. He can even consume only good X or good Y depending which is cheaper to buy. Rob is substituting good X for good Y when Py is less than Px and he is substituting good Y for good X when Px is less than Py. So with the given information we can say that rob's preferences are of perfect substitutes. ​​​​​And mathematically it can represented as,

U(X,Y) = X + Y

He will consume only X when Px < Py

He will consume only Y when Py < Px.