Review Questions

4 What is marginal benefit? What is marginal cost?

The marginal benefit of doing something is the increase in total benefit from doing it a little more. The marginal cost of doing something is the increase in total cost from doing it a little more.

5 State and explain the basic rule of rational choice.

The basic rule is that it is rational to do something until its marginal benefit equals its marginal cost. When the MB is greater than the MC, it is in a person interest to do that thing at least a little more since by doing so the total benefit increases by more than the total cost. On the contrary, when MC is greater than MB doing the thing a little more increases total benefit by less than it increases the total cost and hence decreases the total benefit. Therefore, a person maximizes his benefits by doing the thing up to the point that the marginal benefit equals the marginal cost.

(See footnote 4 on page 242 for some more explanation).

6 What is sunk cost? Why do rational decisions ignore sunk costs?

Sunk costs are costs that you have already paid and cannot recover. "Bygones are bygones."

In rational decision making we compare marginal benefits and costs in order to maximize the net benefit from the considered actions. The sunk cost affects the total benefit, but not the net benefit from a choice – no matter what we do we have to incur it.

In other words, making a rational decision you look at what resources you have now available and not what you had before (no matter how much you regret it).
 
 

Thinking Exercises

7 Suppose that the marginal cost in Figure 4 increases by 20 (changing from 20, 30, 40,..., 160 to 40, 50, 60,..., 180).

a. Show this increase in marginal cost on a graph.

b. How does this increase in marginal cost affect the rational choice of the number of times to take the action?

1. See graph.

 

 


 
 

b. In order to maximize the net benefit, a rational person would decide to take the action 4 times. This is the best choice since now the marginal benefit and marginal cost are equalized for this number of times (both are equal to 70).
 
 

8 Suppose that the marginal benefit in Figure 4 increases by 20 (changing from 100, 90, 80,..., -40 to 120, 110, 100,...,-20).

a. Show this increase in marginal benefit on a graph.

b. How does this increase in marginal benefit affect the rational choice of the number of times to take the action?

a. See graph.



b. In order to maximize the net benefit, a rational person would decide to take the action 6 times. This is the best choice since at this point the marginal benefit and marginal cost are equalized (both are equal to 70).
 
 
 
 

Problems

9 Draw a budget line and show how it changes in response to:

a. A fall in income

b. A fall in the price of the good on the horizontal axis

c. A fall in the price of the good on the vertical axis

a. See graph (a). When income falls, the budget line moves towards the origin.


 
 
 
 

2. See graph (b). When the price of the good on the horizontal axis falls, the budget line rotates to the right with the point on the vertical axis fixed.

 

 


 
 

3. See graph (c). When the price of the good on the vertical axis falls, the budget line rotates upward with the point on the horizontal axis fixed.

10 Suppose that the nominal prices of deodorant and soap both double. What happens to the relative price of deodorant in terms of soap? How does a budget line between them shift?

1. Suppose that your money income doubles along with the nominal prices of all the goods you buy. What happens to your budget line? Do you change what you buy? Explain.

When both prices double, the relative price of deodorant in terms of soap does not change. Suppose the price of deodorant is initially $2, and the price of soap is initially $1. The relative price of deodorant in terms of soap is initially 2=$2/$1. When both prices double the relative price is still 2=$4/$2.

If the income stays constant, the budget line shifts parallelly downwards. It shifts downwards as with the same amount of income we can afford less goods and the shift is parallel as the relative price does not change.

1. When both the prices and income double the budget line does not change. As explained above, doubling both nominal prices does not change the relative price. The budget line does not shift as before and after we can afford the same bundles: although they are twice as expensive we have twice as much money to pay for them.

As an illustration consider the following story. Suppose that some day all shops decide to post their prices in cents instead of dollars. So all the nominal prices get 100 times higher. At the same time your income calculated in cents gets 100 times higher. Clearly, you can afford the same goods after the change as you could before.

11 Judy must take midterm exams today in molecular biology and quantum physics. She can study for only one more hour, and she wants to maximize the total number of points she gets on the two exams added together. She expects the following scores depending on how much she studies each subject (see the table below).

1. Create two new columns to show Judy's marginal benefit and marginal cost from studying biology for 10 more minutes.

1. How much time should she spend studying for each exam? Explain why.
2. Draw Judy's budget line between points on the biology exam and points on the physics exam. Show in your diagram which point on the budget line she should choose.
3. Suppose that Judy has 70 rather than 60 minutes to study. How does this change affect her budget line? How long does she study biology? How long does she study physics? How many additional points could she expect to get by studying the extra 10 minutes?

1. Marginal benefit from studying biology is (7, 6, 5, 4, 3, 2). The marginal cost from studying biology is the opportunity cost of studying less physics, that is the foregone marginal benefit in physics. Thus, the marginal cost of studying biology is (3, 5, 5, 7, 8, 10):

 

 
 
 
 
 
 
 

Minutes Studying  Biology	Expected Score in Biology	Minutes  Studying  Physics	Expected  Score in  Physics	Marginal Benefit from Studying Biology	Marginal Benefit from Studying Biology
0	70	0	55	-	-
10	77	10	65	7	3
20	83	20	73	6	5
30	88	30	80	5	5
40	92	40	85	4	7
50	95	50	90	3	8
60	97	60	93	2	10


 

2. She should spend 30 minutes studying biology, since this is where the marginal benefit and marginal cost are equal. This implies that the remaining 30 minutes she should spend studying physics.

The sum of expected scores is in this case 88+80=168.
 
 
3. See graph. She should choose the point (88,80).

4. The budget line would shift out. Minutes are like Judy's income in this problem.

Now, as we don't know what are the expected scores given she spends all time on one of the subjects, we put some question marks in the table.

The marginal benefit and marginal cost from studying biology are equalized when she spends 30 minutes studying biology and the remaining 40 minutes studying physics. The total expected score from this combination is 88+85=173 (notice that in order to calculate it you should not simply add the numbers in one row). For a comparison, the expected score from studying 40 minutes for biology and 30 minutes for physics is 92+80=172.

As calculated in part b, studying 60 minutes she expects 186 points. So studying the extra 10 minutes she should expect to gain 7 additional points.
 
 
 
 

12. Calculate the marginal benefit and the marginal cost of hours worked. How many hours should you work to maximize your net benefit?

The table shows the calculations:
 

Hours Worked	Total Benefit	Total Cost	Marginal Benefit	Marginal Cost
1	$ 20	$ 8	20	8
2	40	15	20	7
3	58	22	18	7
4	73	29	15	7
5	85	36	12	7
6	96	44	11	8
7	105	53	9	9
8	113	63	8	10
9	119	74	6	11

She should decide to work 7 hours in order to maximize benefits since at that point MB=MC.

13 Explain the economic principle behind the comic strip.

The principle behind the comic strip is the one of sunk costs. The parking ticket plays the role of sunk costs. When deciding if she should go shopping, the ticket does not enter into the cost of doing that action. Leaving the car illegally parked does not matter anymore (assuming that an illegally parked car can get at most one ticket).
 
 
 
 

Questions

A.3 Explain why the absolute value of the slope of an indifference curve shows a person' marginal rate of substitution between two goods.

The marginal rate of substitution between good X and Y is the largest amount of Y that you would be willing to trade away for one unit of X. Now, the absolute of the indifference curve's slope, by definition, shows exactly that. See graph.
 
 

At point A you consume 1 unit of X and 16 units of Y and at point B you consume 2 units of X and 11 units of Y. The marginal rate of substitution is 5. And the slope of the indifference curve is

(change in Y)/(change in X)= 5/1=5.

A.4 Draw a graph with a budget line and indifference curves.

a. Show the person's rational choice on your graph.

b. Explain your graph. Why is the point of tangency the rational choice?

1. See graph. Point A is the rational choice.

 

 



b. Point A is the rational choice because, given his budget line, it is only at this point that this person reaches his highest indifference curve.
 
 

Problems

C.1 Suppose that the total benefit of doing something Q times is :

60Q - Q²

and the total cost of doing something Q times is :

20 + Q²

a. Calculate the marginal benefit and marginal cost.

b. Which choice of Q maximizes net benefit?

c. When you choose Q to maximize net benefit, how large is your net benefit?

a. MB = 60 - 2Q

MC = 2Q

b. Equating MB to MC, we get that Q=15.

2. Replacing Q by 15 in the total benefit and total cost, and subtracting total cost from total benefit, we get that the net benefit is: