Student Number:
QUIZ 2
Section B
Question 1. [4 marks] Diana likes caffeine in the mornings. She is indifferent between drinking coffee or tea, just so long as she gets her desired level of caffeine. Therefore, Diana is indifferent between drinking 2 cups of tea or 1 cup of coffee. Coffee costs $1.50 per cup, whereas tea costs $1.00. Diana has a weekly budget of $15 for “caffeine.” If Diana is maximizing her utility subject to her budget constraint, how many cups of coffee and tea should she buy? Show your work and explain your answer.
Answer:
For Diana, coffee and tea are perfect substitutes. Therefore, it is likely that she will consumer either coffee or tea but not both. If Diana spends all her money on coffee, she can afford 10 cups.
If Diana spends all her money on tea, she can afford 15 cups.
Remembering that Diana requires 2 cups of tea to equal the caffeine in 1 cup of coffee, she would need 20 cups of tea to equal the caffeine of 10 cups of coffee. Since she can afford 10 cups of coffee but not 20 cups of tea (she can only buy 15 at the most), she should buy 10 cups of coffee and 0 cups of tea.
Question 2. [6 marks] Cecilia lives in an economy where people live for two periods. In the current period she works and earns an income of $10,000. In the future period, she has a pension income of $5,500.
a) [1.5 marks] Assuming that Cecilia can not borrow or lend money in the market, write down the budget constraint she faces in solving for her optimal consumption choice. You can write period one consumption as and period two consumption as .
Answer:
, If assuming saving under the mattress.
b) [4.5 marks] Suppose she can borrow and lend at an interest rate of r = 10%. Further suppose that her utility function is . Write out her budget constraint, and solve for the optimal choice of and .
Answer:
Cecilia’s budget constraint is: , or ignoring inequality
Given the form of her utility function, her optimal consumption choice satisfies:
Substituting above in Ceciliea’s intertemporal budget constraint, we get
2