Question

1. Suppose that your utility from the consumption of Coke and Pepsi can be expressed as:

U(C,P) = 2C²P

Where P is the number of units of Pepsi consumed and C is the number of units of coke consumed.

a. Draw indifference curves for U = 100 and U = 1000.

b. If you have $100 to spend on these two goods, and C units cost $2 each and P units cost $1.5 each, draw your budget constraint below.

c. Calculate the utility maximizing quantities of Coke and Pepsi for you under these circumstances.  Show this solution in your diagram above.  What is the marginal utility of pepsi at this point?  The marginal utility of coke?  The consumer’s total utility?

d. Suppose a price war drives the price of Pepsi down to $1.   Calculate the impact of this event on the utility maximizing quantities of Coke and Pepsi for you.  Show this new solution in your diagram.  What happens to your total utility?  Why?

e. Suppose that the federal government decides to take away from your income enough to return you to your old utility level.  How much money would they have to take away?  Explain your answer carefully and think about the impact of the price change on your choices.

Answer 1

Since the utility function is not clear, I am assuming it to be 2C²P because only this function makes sense. If the utility function is different, the same framework can be used to derive the answers.

Budget constraint is

2C+1.5P = 100