# The Concept of Budget Constraint Explained with Examples

A budget constraint is a representation of the quantities and prices of various goods that can be purchased within a specified budget. This story explores the concept of budget constraint with examples.

Buzzle Staff

Last Updated: Mar 6, 2019

Please Remember

For a firm/company, a small budget constraint can be solved by borrowing; however, in the long run, certain other factors need to be considered, like rent, salaries, etc.

THE CONCEPT

● Everyone of us designates a stipulated amount every month from our salary for household expenses, which include expenses for food, clothing, daily utilities, repair, bill payments, etc.

● Now, these expenses heavily depend on your lifestyle and your way of expenditure.

The concept of budget constraint in microeconomics though, is almost based on similar terms.

Example

● Consider a very basic example. Assume that a customer has USD 20 in his hands, and he has to buy apples and oranges.

● Let the price of one apple be USD 2 and the price of one orange be USD 4.

● In this case, the customer has to adjust his purchases such that the total cost adds up to the money he has on hand.

● Let the price of one apple be USD 2 and the price of one orange be USD 4.

● In this case, the customer has to adjust his purchases such that the total cost adds up to the money he has on hand.

Price of one apple P(A) = USD 2

Price of one orange P(O) = USD 4

Price of 4 apples (4A) = 4 X 2 = USD 8

Price of 3 oranges (3O) = 3 X 4 = USD 12

**Therefore, budget constraint = 4A + 3O = 8 + 12 = 20**

P(G1) X Q(G1) + P(G2 + Q(G2) = I

**P(G1) =**Price of one good

**P(G2) =**Price of the other good

**Q(G1) =**Quantity of one good

**Q(G2) =**Quantity of the other good

**I =**total income

● In the graph, the X and Y axes denote the goods, i.e., apples and oranges, respectively.

● The point on the Y axis indicates that the entire income has been spent on oranges. Therefore, the point (0, 5) has been plotted, indicating that the total purchase is 5 oranges.

● Therefore, mathematically, the slope of budget constraint is (-5 / 10), i.e., (-1 / 2). Technically, this means that one orange must be reduced to be able to buy 2 more apples.

IMPORTANT TERMS

Intertemporal Budget Constraint

● It is a term that requires an individual to curtail his expenditure within the available budget, over a long period of time.

● Analyzing an intertemporal budget constraint helps deduce future income and future expenditure.

Example

● Mathematically, assume that over 2 separate time periods, incomes i1 and i2 are earned. The consumptions in these periods are c1 and c2, and the corresponding prices are p1 and p2.

● If an individual does not save any money, his income is going to be equal to his consumption, i.e., i1 = c1 and i2 = c2.

● If an individual does not save any money, his income is going to be equal to his consumption, i.e., i1 = c1 and i2 = c2.

● Now, assume that the consumer has had no expenses in the first period, thus, making his savings equal to his entire income. Let the interest rate be r.

● This will also be the total expenditure if the consumer spends it all, i.e., c2 = i2 + (1+r)i1.

● Thus, the graph will have a point (0, i2 +(1+r)i1) on the Y axis, if all the income from the first period is saved.

● Assuming that the borrowed amount is b1, the value of i2 will be (1+r)b1. Therefore, the maximum expenditure that can take place will be equal to i1 + b1, i.e., i1 + i2/(1+r).

● This graph represents an intertemporal budget constraint, depicting the expenditures and incomes when the consumer chooses to save or borrow.

Utility Function and Marginal Utility

● A utility function helps derive alternate solutions, depending on utility.

● Marginal utility helps determine the quantity of a product, a customer will buy.

Example

● In this scenario, the utility function can be mathematically represented as the (XY)1/2

● Consider the same example of apples and oranges given previously. Now, the budget constraint equation is P(G1) X Q(G1) + P(G2 + Q(G2) = I.

● Consider the same example of apples and oranges given previously. Now, the budget constraint equation is P(G1) X Q(G1) + P(G2 + Q(G2) = I.

● If the price of both the goods is the same, the marginal utility will be equal for both of them, indicating that we need to purchase the same quantity of both the goods.

● Let the price of one orange increases by 3, thus, making it USD 4. In this case, the marginal utility will differ, i.e., the price of one orange is 4 times the price of one apple; therefore, for every orange purchased, we must purchase 4 apples.

● Using these values in the utility function, in the first case (before price changes), the function is (10 X 10) ^ 0.5, which gives us the value 10.

● In the second case, we have (10 X 2.5) ^ 0.5, which gives us the value 5; half of 10.

Indifference Curve

● Indifference curves are obtained when, for a given number of choices, the value of the utility function is the same.

● This equation can be optimized further in order to obtain the consumer's demand curves.

Example

● Use the equation from the graph in the previous example, i.e.,

● From the equation, we can write:

● Therefore,

[(X)1/2] [((I - Px) / Py)1/2]

**PxX + PyY =**I and let the utility function be**U =**(XY)1/2.● From the equation, we can write:

**Y =**(I - Px) / Py. Substitute this in the utility function.● Therefore,

**U =**(XY)1/2[(X)1/2] [((I - Px) / Py)1/2]

(1/2)(X)-1/2 [((I - Px) / Py)1/2] + (1/2)(X)1/2 [((I - Px) / Py)-1/2] (-(Px) / (Py))

● Considering the utility function as zero, we obtain

(1/2) [((I - Px) / Py)1/2] [(X)1/2] = (Px) / 2(Py) [(X)1/2] [(X)1/2] [((I - Px) / Py)1/2]

● Solving this equation, we get X = I/2(Px) and Y = I/(Py)

● Using these values, we can obtain different demand curves, by changing the value of I.

BUDGET CONSTRAINT AND CHANGING PRICES

● When the cost of one product increases compared to the other, the budget constraint rotates in a clockwise direction.

● The change in either of the goods causes the budget curve to move closer to the origin, introducing new intercepts.

Effect of changing prices on budget constraint

**Budget constraint with changes**

**Budget constraint with x intercept**

**Budget constraint with y intercept**