Imagine an individual who has the following Cobb-Douglas Utility function:
U = x10.5x20.5
This person has an income of $40,000. Suppose the price of Good 1 (Fruit) is p1 = 5
and the price of Good 2 (Bread) is p2 = 4.
a) Determine the optimal consumption bundle for this individual. How
much utility do they get from consuming this bundle? Construct a graph which
illustrates this situation.
b) Suppose that this person gets a promotion at work and their income
increases to $50,000. What is this consumer's new optimal consumption bundle?
Show whether this consumer is going to better off or worse off. Construct a graph
which illustrates this situation.
c) The government is concerned that people are eating too much bread
and not enough fruit. They are considering two policies:
1. A tax on bread equal to $1 per loaf of bread consumed.
2. An income tax of $8,000, and a subsidy on fruit of $1 per fruit purchased.
Answer the following questions for both of these policies. (Note: The income
remains at the new higher value of $50,000)
i) What is the new optimal consumption bundle?
ii) What is the resulting utility of the consumer?
iii) What is the net amount of money collected by the government?
d) Based on your analysis, which of two policies would you recommend
that the government pursue? Justify your answer.