Topic V - Short Answer Questions

1.Complete the following table:

Qx        TUx          MUx

0                            0
1          1000         1000
2          1800          800
3          2100          300
4          2180            80

2. Complete the following table:

Qx        TUx         MUx

0                           0
1           0              0
2          100          100
3          100           0
4          180          80

Can you think of any goods that might lead to such a strange set of preferences? Goods that only have usefulness in pairs such as shoes.

3. If total utility from good X were to reach a maximum and then start to decline for additional units of good X, what would this imply about the marginal utility from additional units of good X? Make up a numerical example to show this.

It would imply a negative marginal utility - example
Qx         TUx         MUx

1            100          100
2            160            60
3            170           10
4            140          -30
4            100          -40

4. Assume Z is a complement to good X, and Y is a substitute for good X. Also assume Joe Brown is currently maximizing utility with respect to consumption of each of these goods. What might we expect to happen to Joe Brown's purchases of X, Y, and Z if the price of good X falls? Why?

If Joe is maximizing then the equal marginal rule is satisfied -- MUx/Px = Muy/PY = Muz/Pz. If the price of good X falls, then the MUx/Px increases. This would lead Joe to buy more X. If Joe buys more of X, then he buys more of Z because Z is a complement to X and he buys less of Y, since X is a substitute for Y.

5. Assume Z is a complement to good X, and Y is a substitute for good X. Also assume Joe Brown is currently maximizing utility with respect to consumption of each of these goods. What might we expect to happen to Joe Brown's purchases of X, Y, and Z if Joe's income increases from $1,000. per month to $1,500 per month? Why? State precisely what assumptions your answer depends upon.

If Joe is maximizing then the equal marginal rule is satisfied -- MUx/Px = MUy/PY = MUz/Pz and Joe's purchases of X, Y, and Z adds up to $1000 per month. When Joe's income increase the equal marginal rule is still satisfied, but he is not spending all of his income. What we know is that Joe will buy more of goods that are normal goods and less of goods that are inferior goods. In this case we know that Joe will buy more of some of these goods, but without knowing what is normal and what is inferior - we can't say more. Except, we can say if he buys more X, he will buy more Z; and if he buys less X, he will buy less Z.