μMicroeconomics LabGRAPHICAL EXPLORATIONSOffer Curve Lab ↗

EXPLORE · ADJUST · EXPLAIN

Build a budget constraint

Add a price tier, move a kink, and see exactly which bundles remain affordable.

Budget & price tiers

Segment 1slope −1

Segment 2slope −2

Segment 3slope −3

Up to 5 kinks. Prices apply only to units within each tier; earlier units keep their original price.

Your feasible set

The shaded area includes every affordable bundle.

Piecewise linear budget constraint and feasible set0012.62325.34637.96950.69263.2115K1K2Good xGood y
Maximum x55
Maximum y100
Active segments3

The analytical budget

Cumulative spending across price tiers
pyy+E(x)≤m,x,y≥0E(x)=∑j=1Jpjmax⁡ ⁣{0,min⁡(x,kj)−kj−1}k0=0,kJ=∞\begin{aligned}p_y y+E(x)&\le m,\qquad x,y\ge0\\ E(x)&=\sum_{j=1}^{J}p_j\max\!\left\{0,\min(x,k_j)-k_{j-1}\right\}\\k_0&=0,\qquad k_J=\infty\end{aligned}
0 ≤ x ≤ 20
y≤100−0−1(x−0)1y\le\frac{100-0-1(x-0)}{1}
20 ≤ x ≤ 45
y≤100−20−2(x−20)1y\le\frac{100-20-2(x-20)}{1}
45 ≤ x < ∞
y≤100−70−3(x−45)1y\le\frac{100-70-3(x-45)}{1}
Each piece has slope −pⱼ/pᵧ. A higher marginal price makes the next segment steeper. A kink beyond the x-intercept cannot be reached with this income; its formula still describes the tariff.

Try reversing the price order. A quantity discount can make the feasible set nonconvex. A zero-price tier creates a horizontal segment; the final price stays positive so maximum x is finite.