diff --git a/freeride/affine.py b/freeride/affine.py
index 76578cc..a34e5e6 100644
--- a/freeride/affine.py
+++ b/freeride/affine.py
@@ -899,12 +899,22 @@ def equation(self, inverse=False):
             latex_str += r"\end{cases}"
             return f"${latex_str}$"
 
-    def price_elasticity(self, p, delta=.000001):
+    def price_elasticity(self, p, delta=.000001, atol=1e-12, rtol=1e-9):
         q = self.q(p)
         pt = np.array([p,q])
-        if self.intersections and np.any(pt == self.intersections, axis=1).max():
-            below = self.price_elasticity(p - delta)
-            above = self.price_elasticity(p + delta)
+        intersections = np.asarray(self.intersections)
+        is_kink = (
+            intersections.size > 0
+            and intersections.ndim == 2
+            and intersections.shape[1] == 2
+            and np.any(
+                np.isclose(pt[0], intersections[:, 0], atol=atol, rtol=rtol)
+                & np.isclose(pt[1], intersections[:, 1], atol=atol, rtol=rtol)
+            )
+        )
+        if is_kink:
+            below = self.price_elasticity(p - delta, delta=delta, atol=atol, rtol=rtol)
+            above = self.price_elasticity(p + delta, delta=delta, atol=atol, rtol=rtol)
             s = f"\nElasticity is {below:+.3f} below P={p} and {above:+.3f} above."
             raise ValueError("Point elasticity is not defined at a kink point."+s)
         else:
diff --git a/tests/test_curves.py b/tests/test_curves.py
index 5d0bc2d..517388f 100644
--- a/tests/test_curves.py
+++ b/tests/test_curves.py
@@ -126,6 +126,29 @@ def test_horizontal_sum(self):
         self.assertIsNone(active[2])
 
 
+class TestAffinePriceElasticityKinks(unittest.TestCase):
+    def setUp(self):
+        d1 = Demand(12, -1)
+        d2 = Demand(6, -0.5)
+        self.kinked_demand = d1 + d2
+        self.kink_p = self.kinked_demand.intersections[0][0]
+
+    def test_exact_kink_input_raises(self):
+        with self.assertRaisesRegex(ValueError, "kink point"):
+            self.kinked_demand.price_elasticity(self.kink_p)
+
+    def test_near_kink_input_does_not_raise(self):
+        elasticity = self.kinked_demand.price_elasticity(self.kink_p + 1e-7)
+        self.assertTrue(np.isfinite(elasticity))
+
+    def test_floating_point_kink_representation_raises(self):
+        # 0.1 + 0.2 is not exactly representable; scaled here it lands
+        # extremely close to the true kink price of 6.
+        p_with_fp_noise = (0.1 + 0.2) * 20
+        with self.assertRaisesRegex(ValueError, "kink point"):
+            self.kinked_demand.price_elasticity(p_with_fp_noise)
+
+
 class TestSurplusAndRevenue(unittest.TestCase):
 
     def setUp(self):