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| A budget contraint in terms of two goods, ''x'' and ''y'', is usually characterized as a line. The line is defined by the equality ''xP,,x,, + yP,,y,, = m''; wherein | A budget contraint in terms of two goods, ''x'' and ''y'', is characterized as a line. The line is defined by the equality ''xP,,x,, + yP,,y,, = m''; wherein |
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| Also, the budget constraint is [[LinearAlgebra/Orthogonality|orthogonal]] to the price vector. ---- == Non-linear Budget Sets == The above forms of budget constraints are linear. In some cases, the constraint is not constructed in this shape. * Under autarky, the budget constraint conforms to the [[Economics/ProductionPossibilityFrontier|PPF]]. * Rationing creates a piecewise budget constraint; it operates as normal up to some threshold where it becomes constant. * Progressive (and regressive) taxing create complex piecewise budget constraints. |
Budget Constraint
A budget constraint is a line or plane that limits possible consumer choices.
Bivariate
A budget contraint in terms of two goods, x and y, is characterized as a line. The line is defined by the equality xPx + yPy = m; wherein
i is the quantity of good i itself
Pi is the price of good i
m is the available income that can be spent
The intercepts of this line are m/Px and m/Py (on the x- and y-axes respectively).
The slope of this line is -Px/Py. This is generally referred to as the marginal rate of transformation (MRT).
Multivariate
A budget constraint is defined by the equality of some income constant m to the dot product of the price and quantity vectors p and q. (Recall that the dot product of two vectors like [x y] and [Px Py] is xPx + yPy.)
Also, the budget constraint is orthogonal to the price vector.
Non-linear Budget Sets
The above forms of budget constraints are linear. In some cases, the constraint is not constructed in this shape.
Under autarky, the budget constraint conforms to the PPF.
- Rationing creates a piecewise budget constraint; it operates as normal up to some threshold where it becomes constant.
- Progressive (and regressive) taxing create complex piecewise budget constraints.