SLOPE OF BUDGET LINE

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Learning Contents:                                                            

·          Slope of Budget Line and Price Ratio

·         Properties of Budget Line

·         Understanding the slope of the budget line through a budget equation.

Slope of Budget Line/Price Line

As we have studied in previous topics that budget line shows the various combinations of two goods that consumer can afford to purchase when the price of two goods and the income is given.

 In simple words, the slope of the budget line indicates the ratio of units sacrificed of good Y to acquire specific units of good X at a given market price is also known as market rate of exchange.

(When expressing the slope of the budget line in terms of quantity)

 Note: Slope of Budget line is also known as price ratio.

Price Ratio

When expressing it in terms of price, it is simply the ratio of the prices of two goods or the price of the good on the horizontal or X-axis divided by the price of the good on the vertical or Y-axis., also known as the price ratio. 

Where: PX is the price of Good- X; and
PY is the price of Good -Y.

(When expressing the slope of the budget line in terms of price)

Properties of Budget Line

1.Budget Line slopes downward

Budget Line slopes downward as consumption of  both the goods are inversely related to each other i.e. a consumer   has to sacrifice the quantity of good A in order to get an additional quantity of good B   or  simply, it means a consumer can buy more of a good only when he sacrifices the other good i.e. opportunity cost exists. The opportunity cost of something is the value of the next-best alternative given up in order to do get it. So, the negative relation between consumption quantities of two goods cause the budget line to slope downwards.

 

Please refer to the example given below to get a practical overview of a downward sloping budget line.

Suppose a consumer has a total income of ₹18 which he can spend on the purchase of ice creams and cookies. Further, the price of each cookie is ₹2 and the price of each ice cream is ₹3. The budget constraint indicates that a consumer can spend on the various combinations of ice cream and pizza not more than his available income. If a consumer spends all of his income on cookies (and none on ice cream), the consumer can buy 18/2 = 9 units of cookies, this represents by the point (0, 9) on the graph or we call it y-intercept. Whereas, if he spends all of his income on ice creams (and none on cookies), the consumer can buy 18/3 = 6 units of ice creams. This is represented by the point (6, 0) on the graph or we call it x-intercept.

In Figure 1.1, the number of ice creams a consumer will buy is shown on the horizontal axis, while the number of cookies he will buy is on the vertical axis. After that, we plot all the combinations on the graph. The easiest way is to find the combinations so as to plot the intercepts. Each intercept gives an extreme connecting point that indicates a consumer spends all his income on either ice cream or cookies and by connecting these two extreme combinations A and D we get a straight budget line and also we can find some other combinations that a consumer can afford along this budget line. Below mentioned table 1.1 shows various combinations of ice creams and cookies which a consumer can afford when his budget is ₹18.


1.1 Budget Schedule

 

Combn

 

Units of ice creams

 

Units of cookies

 

Budget Allocation

(Amount in ₹)

 

Slope of the budget line/

Market rate of exchange

A

0

9

3*0+2*9=18

------

B

2

6

3*2+2*6=18

3/2=1.5

C

4

3

3*4+2*3=18

3/2=1.5

D

6

0

3*6+2*0=18

3/2=1.5


Figure 1.1 Graphing the Budget Line



2. Budget Line is straight

Budget line is straight as it has a constant slope or constant market rate of exchange along its entire length that means the ratio of sacrificing good to gaining good remains constant across all the combinations lying on the budget line. Looking at the above budget schedule 1.1 we see that the slope is 1.5 across all the combinations from A to D.

3. Real Income Line

The budget line is based on the principle of income and the spending capacity of a consumer. It states that a consumer can purchase all the combinations of goods that cost less or equal to his income.

4. Tangent to Indifference Curve: The indifference curve touches the budget line at a point and this point is known as the consumer’s equilibrium.


Calculating the slope of the budget line through budget equation based on the above example

 The budget equation represents the budget constraint or limited income to be spent on two different goods by the consumer. A budget equation can be represented as below:

Y= PIQI+PCQC

Where,

Y= Total budget/total income/total expenditure

PI=Price of ice cream

QI=Quantity of ice cream

PC=Price of cookies

QC=Quantity of cookies

Calculating  slope and intercept of the budget using the budget equation:

 Y= PIQI+PCQC

=>Y- PIQI= PCQC

  =>Y- PIQI÷PC= QC

  =>Y/PC- PIQI/PC= QC








Note- Numerator will always have a negative value as it shows the number of units to be sacrificed. However, for analysis, absolute value (ignoring± signs) is always considered.


Let’s take a Quiz

Choose the Correct Answer

1. The slope of the budget line is indicated by

a. Price of Good -X/ Price of Good-Y

b. Price of Good -Y/ Price of Good-X

c. Price of Good –X=Price of Good-Y

d. all of these

2. Which of the following represents the properties of budget line?

a. slopes downward

b. straight line

c. based on real income and purchasing power

d. All of these

3. Suppose a consumer has ₹100 to spend on two goods, chocolates, and ice creams. If the price of each chocolate is ₹20 and the price of ice cream is ₹15 each, which of the following combinations is unaffordable to the consumer?

a. 0 chocolates and 0 ice creams

b. 2 chocolates and 4 ice creams

c. 5 chocolates and 0 ice creams

d. 0 chocolates and 7 ice creams

4. Which of the following represents best as a budget equation?

a. Y= P1QI+P2Q2

b. Y= P1QI-P2Q2

c. Y= P1Q2-P2Q1

d. Y= P1Q2+P2Q1

5. The rate at which the consumer can substitute Good-1 for Good-2 tends to decline as we move downward along the price line.

a. True

b. False

6.  Jack spends all his income on two goods: comic books, which costs ₹2 each, and candy bars, which cost ₹4 each. The graph below shows Jacks’s budget constraint, with comic books on the vertical axis and candy bars on the horizontal axis. 




Based on this information, what is jack’s income?

a. ₹12

b. ₹48

c. ₹72

d. ₹20


7. Jamie’s income is ₹24, and she spends the entire amount on pizza and cookies. The graph below shows her budget constraint, with pizza slices on the vertical axis and cookies on the horizontal axis.

 




 










Based on this information, what are the prices of pizza slices and cookies?

a. Pizza slices are ₹4; Cookies are ₹2

b. Pizza slices are ₹3; Cookies are ₹4

c. Pizza slices are ₹3; Cookies are ₹2

d. Pizza slices are ₹3; Cookies are ₹4

 

Answer Key

1. a 2.d 3.d 4.a 5.b  6.b 7.c

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Comment if you have any questions.

 


 

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