A rational consumer is consuming only two goods, Good X and Good Y. The
prices of the goods are Rs. 20 and Rs. 10 respectively. Her total money income
is Rs. 200. Answer the following questions using the given information:
a. State her Budget line equation.
b. State the slope of the Budget line of the consumer.
c. If she decides to spend her entire income on Good Y, how many units of
Good Y can she buy?
d. What is the slope of budget line?
Answers
Explanation:
Let X
1
denote Good-1 and X
2
denote Good-2.
P
1
=Rs4,P
2
=Rs5,Y=Rs20
(i) P
1
X
1
+P
2
X
2
=Y
4X
1
+5X
2
=20
Thus, the equation of the budget line is 4X
1
+5X
2
=20.
(ii) We know equation of the budget line is:
P
1
X
1
+P
2
X
2
=Y
If the consumer spends her entire income on Good-1, then
X
2
=0
P
1
X
1
=Y⇒4X
1
=20
X
1
=5
Thus, the consumer can buy 5 units of Good-1 if she spends her entire income on that good.
(iii) If the consumer spends her entire income on Good-2, then
X
1
=0
P
2
X
2
=Y⇒5X
2
=20
X
2
=4
Thus, the consumer can buy 4 units of Good-2 if she spends her entire income on that good.
(iv) Slope of budget line =
P
2
P
1
=
5
4
.
( a ). The budget line shows all the different combinations of the two commodities that a consumer can purchase, given his money income and the price of two commodities.
The equation of a budget line is given by:
M=P
X
.Q
X
+P
Y
.Q
Y
.
Where, M = Money income of the consumer; P
X
= Price of Good-X; P
Y
= Price of Good-Y; Q
X
= Quantity of Good-X; Q
Y
= Quantity of Good-Y.
Supposing a consumer has an income of Rs 40 to be spent on apples and oranges. Price of an orange is Rs 5 and an apple is Rs 10. With his given income and given prices of apples and oranges, the different combinations that a consumer can get of these two goods are shown in the following table:
Combination Income (M) Oranges Apples
A 40 8 0
B 40 6 1
C 40 4 2
D 40 2 3
E 40 0 4
A consumer can purchase any of the above combinations in accordance with the budget line equation.
( b ). The slope of the budget line is the amount of good 2 given up to have one more unit of good 1. The price of one unit of good 1 is P1. ... So, with the P1 amount, of good 2 could have been bought. Thus, the consumer must give up units of good 2 to obtain one extra unit of good 1, i.e. the slope of the budget line is.
( c ). Decisions within a budget constraint
Another approach to maximizing utility uses indifference curves (sometimes called utility curves) and budget constraints to identify the utility optimizing combination of consumption. Read about this method in this article.
Key points
The budget constraint is the boundary of the opportunity set—all possible combinations of consumption that someone can afford given the prices of goods and the individual’s income.
Opportunity cost measures cost in terms of what must be given up in exchange.
Marginal analysis is the process of comparing the benefits and costs of choosing a little more or a little less of a certain good.
The law of diminishing marginal utility indicates that as a person receives more of a good, the additional—or marginal—utility from each additional unit of the good declines.
Sunk costs are costs that occurred in the past and cannot be recovered; they should be disregarded in making current decisions.
Utility is the satisfaction, usefulness, or value one obtains from consuming goods and services.
( d ). The slope of the budget line is the amount of good 2 given up to have one more unit of good 1. The price of one unit of good 1 is P1. To have one more unit of good 1, therefore, consumption of good 2 must be reduced by P1 amount.