Economics 101
Fall 2003
Answers for Practice Questions 5

1. Suppose one consumer wants to purchase clothes and books. Choose the necessary information to study the consumer’s choice.
(a) income of the consumer
(b) price of cloth
(c) price of books
(d) preferences of the consumer
(e) all of the above

(e): Consumers maximize utility given the budget constraint. So, we need to know the preferences (utility) and the budget line(prices and income). 

2. Which is true for indifference curves?
(a) Lower indifference curves are prefered to higher ones.
(b) Along one I.C., every point represents a constant level of satisfaction.
(c) In general, I.C.s are upward sloping.
(d) Some I.C.s can cross, if income is very high.
(e) I.C.s are bowed inward, because the opportunity cost is increasing.

(b): (a) Higher ICs are prefered to lower ones. 
      (c) ICs are downward sloping.
      (d) ICs cannot cross.
(e) ICs are bowed inward, because consumers prefer  variety. 

3. Draw the budget line in each case. For each case, calculate the slope and then compare cases (b) through (f) to case (a).

	income	price of X good	price of Y good	
   (a)	100	10	5	
   (b)	100	10	20	
   (c)	100	5	5	
   (d)	200	10	5	
   (e)	50	10	5	
   (f)	200	20	10	

good Y

good X

20

10

(a) the slope is –2.

(b): the slope is –1/2.Note that budget line pivots in toward the origin while maintaining the same X-intercept.

good Y

good X

20

10

5

(c): the slope is –1.Note that budget line pivots outward away from the origin while maintaining the same Y-intercept. 

good Y

good X

20

10

20

(d): the slope is –2.Note that the slope is the same as (a). 

good Y

good X

20

10

20

(e): the slope is –2. This is the same slope as (a) and (d). 

good Y

good X

20

10

10

5

(f): the slope is –2. And the budget line is the same as (a). If the income and the prices are changed with the same propotion, then the budget line does not change. 

good Y

good X

20

10

4. Jack spends all of his income on books and CDs. The price of one book is $30 and the price of one CD is $20. Then, at his optimal choice of consumption, what’s the value of the slope of the indifference curve? (put the books on the X-axis and CDs on the Y-axis.) 
(a) –2/3
(b) –3/2
(c) –20
(d) –30
(e) It depends on the size of his income.

(b): MRS is the slope of the IC. At the optimal choice, the MRS should be equal to –P x /Py . So, MRS must be –3/2. 

5. The utility of John is represented by U(x,y)=x*y. This implies, if he consumes 4 units of x and 5 units of y, then his utility(degree of satifaction) is 4*5=20. Then find at least 5 choices which give him the utility of 100, and draw the indifference curve. 

For example, you can pick (1,100), (2,50), (4,25), (5,20), (10,10), (20,5), (25,4), (50,2), (100,1). 

good Y

20

10

5
4

2

  20    25

good X

50

10

5

6. Determine which of the following are true or false.
(a) If X and Y are normal goods, then the income-consumption line is upward sloping.
(b) If X is an inferior good, then Y can be an inferior good also.
(c) The income-consumption line represents the relationship of the optimal choice to a change in the price of the good on the X-axis. 
(d) If Y is an inferior good, then X must be a normal good. 
(e) If X is an inferior good, then the optimal choice is not on the budget line.

(a): true. Consumption of both goods increases as income increases. So, we have an upward sloping income-consumption line.
(b): false. It is impossible for both goods to be inferior goods. So if X is inferior good, then Y must be normal good. 
(c): false. The income-consumption line represents the relationship of the optimal choice to a change in income. The price-conumption line represents the relationship of the optimal choice to a change in the price of one good.
(d): true. See (b).
(e): false. The optimal choice must be on the budget line. Otherwise, the consumer does not spend all of their income.

7. Which of the following is true from the following graph?
(a) The consumer prefers A to C.
(b) The optimal choice is D.
(c) The consumer is indifferent between A and D.
(d) The optimal choice is B.
(e) C is prefered to B. 

(c): (a) C is preferred to A, because C is on the higher IC.
(b) The optimal choice is C.
(c) A and D are on the same IC, so the individaul is indifferent between the two choices.
(d) B is not affordable for the consumer, as B is above the budget line.
(e) The consumer is indifferent between C and B, because they are on the same IC. 

8. One consumer’s indifference curves and budget line are given in the following graph. A is the optimal choice given the budget line. If the income increases, the consumer chooses a point which is located northwest side of A.(There is no change in the prices.) What can we say about good X and good Y? 

Since income increases, the new optimal choice gives the consumer higher utility than the original optimal choice. So, we know that the new choice is above the IC which goes through A. Then the new choice is around B. For the new optimal choice, the consumption of X decreases, and the consumption of Y increases. Therefore, we can say that X is an inferior good and that Y is a normal good. 

B