Alteration in Budget Set

What is Slope of the Budget Line? What is Price Ratio?

Introduction

In previous session, we discussed about the Budget Set. All the combination or bundles of goods and services available to the consumer for consumption after due consideration of the income of the consumer and the prices of the goods and services, is called the Budget Set. We also discussed several examples with their graphical representation and saw the structure of Budget Line. The line in the graphical representation on which all the combination or bindles of goods and services lie with assuming that the cost of those goods and services is exactly equal to the total income of the consumer is known as the Budget Line. Throughout we noticed that the deciding factors for a consumer to get a Budget Set for consumption, showing all possible combination or bundles of goods and services are income of the consumer and the prices of the goods. In real world, both these factors are subject to change and in some cases even frequently. So it becomes very important to understand that what happens of any of the above factor changes and what impact it makes on the Budget Set.

But before we move on to discuss the change in Budget Set, it is very important to understand the slope of the budget line and its derivation.

What is Slope of the Budget Line? What is Price Ratio?

For simplicity let us assume that the income of the consumer is M and in continuation of last session we take two fruits available for consumption which will make a consumption bundle. The two fruits are Apples and Bananas. The price per unit of Apple is p1 and the price per unit of banana is p2. At the same time, quantity demanded by the consumer for apple is q1 and quantity demanded by the consumer for banana is q2. So the total cost of apples comes as p1q1 and total cost of bananas comes at p2q2. And as we know the total income of the consumer is M which means that the total cost of apples and bananas should be less than or at max equal to the income that is M. We can mention it as

p1q1 + p2q2 ≤ M

We discussed in previous session that the above inequality is known as Budget Constraint.

And we get a graphical representation as follows.

Slope of the Budget Line

The origin of the Budget line can be traced to the price ratio between the goods out of which the combination or bundles for consumption is made of. Here it is made of Apple and Banana. So price of the apple is p1 and the price of the banana is p2.

The budget line represents those combination or bundles which costs the entire income or budget of the consumer. Now if the consumer wants to have additional quantity of any of the good in the consumption bundle, consumer will have to give up some amount of thee other good. If the consumer wants an additional apple, then some amount of bananas will need to be given up. Now come the question how much of the bananas, consumer will have to give up to get an additional apple? This depends on the prices of apples and bananas.

Price per unit of apple is p1 and thus the consumer will need to decrease the expenditure on bananas by p1 amount to get an additional quantity of apple. With p1 amount, the consumer can buy p1/p2 quantities of bananas. Thus when the consumer wants an additional quantity of apple assuming total income is being spent to buy those goods, consumer will need to give up p1/p2 quantities of bananas. Summing up, given the market prices of apples and bananas, the consumer can substitute apples for bananas at the rate of p1/p2.

Similarly, the slope of the budget line measure or describes the amount of change in bananas required per unit change in apples for all the point on the budget line. 

The equation for the above points on the budget lines are

1     1) p1q1 + p2q2 = M

2     2) p1(q1 + ∆q1) + p2(q2 + ∆q2) = M

Subtracting 1 from 2 we get;

p1∆q1 + p2∆q2 = 0

Rearranging the above we get

∆q2 = (-) p1

∆q1         p2

Thus the absolute value of the slope i.e., p1/p2, of the budget line measure or describes the amount of change in bananas required per unit change in apples for all the point on the budget line.

Alteration in Budget Set

Continued…

The deciding factors for a consumer to get a Budget Set for consumption, showing all possible combination or bundles of goods and services are income of the consumer and the prices of the goods. In real world, both these factors are subject to change and in some cases even frequently. So it becomes very important to understand that what happens of any of the above factor changes and what impact it makes on the Budget Set.

When the income of the consumer or price of the goods changes, the available combination or bundles also changes.

Case 1 – The income of the consumer changes keeping the prices of goods unchanged

The income of the consumer changes from M to M’ and hence the common equation of the budget line comes up as

P1q1 + p2q2 = M’

Now there can be two possibilities, either the income of the consumer increases or decreases.

A – Income of the consumer increases i.e., M’>M

Even after the increase in consumer’s income, the slope of the budget line remains same but there is an outward shift in the budget line changing the vertical intercept and horizontal intercept from M/p2 to M’/p2 and M/p1 to M’/p2 respectively.

Thus it means that as the income of the consumer increases, the consumer can buy more at prevailing market prices.

B – Income of the consumer decreases i.e., M’<M

Even after the decrease in consumer’s income, the slope of the budget line remains same but there is an inward shift in the budget line changing the vertical intercept and horizontal intercept from M/p2 to M’/p2 and M/p1 to M’/p2 respectively.

Thus it means that as the income of the consumer decreases, the consumer can buy less at prevailing market prices.

Case 2 – The price of the one of the goods changes but income remains unchanged

Let us say that the price of the apple change from p1 to (p’1) but the price of banana and income remains the same at p2 and M respectively.

The new equation for the budget line would come up as

p’1q1 + p2q2 = M

Now there can be two possibilities, either the price of the apple increases or decreases.

A – Price of the apple increases i.e., p’1>p1

Here, the vertical intercept for the new budget line remains the same but the slope of the budget line as well as the horizontal intercept have changed. As the price of the apple increased, the slope of the budget line becomes steeper pivoting towards the vertical intercept from horizontal intercept denoting that the absolute value of the slope of budget line increased.

B – Price of the apple decreases i.e., p’1<p1

Here, the vertical intercept for the new budget line remains the same but the slope of the budget line as well as the horizontal intercept have changed. As the price of the apple decreased, the slope of the budget line becomes flatter pivoting outwards from vertical intercept denoting that the absolute value of the slope of budget line decreased.

Conclusion

In this session, we discussed the Budget Set and Budget line in detail. We discussed how the changes in the factors namely the income of the consumer and prices of the goods, deciding the consumption bundle, changes the available bundles for consumption in the budget set. We saw how these changes are manifested in the graphical representation with the shifts in the Budget Line.