Budget

Budget line is the locus of various combinations of two goods x and y which total money expenditure remains the same. In other words the budget line or price line includes various combinations of two goods x and y which can be purchased by the given budget or money outlay of the consumer. All points along the budget line represents equal amount of total expenditure of the consumer.

    The budget line is represented by an equation of the budget line. Let Qx and Qy be the amounts of commodity x and y that the consumer purchases within the given money income M with the corresponding prices Px and Py.

Now budget allocated in x=Px.Qx

Also budget allocated in y=Py.Qy

Total budget = budget allocated in x + budget allocated in y

Py.Qy=Px.Qx+M………………….(1)

    In the form of quantity y= ((Px.Qx)/Py) +(M/Py)…………….(2)

 Or Qy = (M/Py)-(Px.Qx/Py)

Slope (m) =-PxQx/Py

The budget line can be constructed with the ratio of two extreme points. If entire budget is spend on commodity x, then quantity purchase of Y₁Qy=0

Now equation (1) becomes,

0=(-Px.Qx/Py)+(M/Py)

Or –PxQx + M=0

Or Qx=M/Px

One point (M/Px , 0) is determined

Likewise if entire budget is spend on commodity y, i.e. Qx=0 then equation (2) with the help of two extreme on commodity x then Y+Y becomes

Y=(-Px.X0/Py)+(M/Py)

Or Qy= M/Py

Another point (0, M/Py) is determined

When two extreme points (M/Px, 0) and (0, M/Py) are plotted on a graph measuring units of x along x axis and that of y along y axis and solving two points we obtain a budget line as shown below.

Equation of budget line is

M= Px.Qx + Py.Qy

Slope (m)= -Px/Py

In the figure AB is the budget line whose equation is M=Px.Qx + Py.Qy having slope (m)= -Px/Py. Slope of the budget line AB is negative, we can say that budget line always slopes downward having negative slope. The rational consumer should choose any point in between the points A and B along the budget line AB. Weather consumer chooses point C or D or any other point In between A and B his total money expenditure remains unchanged at M. point E inside the budget region of the consumer is attainable but consumers allocated budget is not fully spend while buying combination E. so consumer cannot maximize his level of satisfaction at point E though it is attainable.  Another point F lying outside the budget region is not attainable because consumer total budget is insufficient to buy combination f.