Chapter 10, Problem 4P

To determine

Concept introduction:

Budget Line: It is defined as the combination of all goods that a consumer can buy exhausting his all income. Formula for the budget line is:

Here,

• is the quantity of good X.
  
• is the quantity of good Y.
  
• is the total income.
  
• is the price of good X.
  
• is the price of good Y.
  

Marginal Utility: It is defined as the change in the total utility due to a change in the additional unit of a good. It may be diminishing, increasing, or constant.

Or

Here,
• is the marginal utility.
  
• is the total utility.
  
• X is the quantity of any good.
• N is the number of goods.

Marginal Utility per dollar: It is the ratio of marginal utility to that of the price of a good. The formula to calculate the marginal utility per dollar is:

Here,

• is the marginal utility per dollar.
  
• is the price of good X.
  

Maximizing utility in the case of two goods: It states that the equilibrium level of consumption of two goods for a consumer is achieved when the marginal utility per dollar of the two goods are equal. This means that the following conditions must be fulfilled:


Here,
• is the marginal utility of good X.
  
• is the marginal utility of good Y.
  
• is the price of good X.
  
• is the price of good Y.
  

Explanation of Solution

a. Mr. Bernie’s consumption bundles of notebooks and mp3s.

Given that the total income of Mr. Bernie is the price of mp3 and notebook isand respectively. Then the consumption bundles of Mr. Bernie suppose that he spends all his income is calculated as follows:

Quantity of mp3s	Quantity of notebooks	($)
10	0	20
8	1	20
6	2	20
4	3	20
2	4	20
0	5	20
Table(1)

From the above table, the bundles which can be consumed by Mr. Bernie, if he spends all his income areand

The below graph shows the budget line of Mr. Bernie based on the above table:

Fig 1

• The above figure shows the various combinations of goods which Mr. Bernie can consume spending all his income.

• The Quantity of Mp3s is represented by the x-axis and the quantity of notebooks is represented by the y-axis.

• When he spends all his income on the mp3s, the bundle isif he spends all his income on the notebook, then the bundle is

Conclusion:

Thus, Mr. Bernie’s consumption bundles are calculated using table 1 and shown in the fig 1.

b. Mr. Bernie’s Marginal Utility of mp3s and notebook.

The below table shows the calculation of marginal utility and marginal utility per dollar. The formula used for the calculation is given in the concept introduction.

Quantity of mp3	Total utility of mp3	Marginal utility of each mp3	Marginal Utility per dollar
0	0	-	-
2	28	14	7
4	52	12	6
6	72	10	5
8	96	12	6
10	108	6	3
Table(2)

Quantity of notebooks	Total utility of notebooks	Marginal utility of each notebooks	Marginal Utility per dollar
0	0	-	-
1	32	32	8
2	60	28	7
3	84	24	6
4	104	20	5
5	120	16	4
Table(3)

Conclusion:

Thus, marginal utility and marginal utility per dollar are calculated above.

c. Utility maximizing principle.

Fig 2

• In the figure 2, the x-axis represents the quantity of notebooks in the right direction and the quantity of mp3s in the left direction.

• The y-axis represents the marginal utility per dollar. In the figure 2, it is clearly observed that the marginal utility per dollar of both goods are equal at 3 notebooks and 8 mp3s. So, this is the optimum bundle.

Conclusion:

Thus, the optimum bundle is which means 8 mp3s and 3 notebooks.