BUG: PeriodDtype incorrectly caching different DateOffset freqs

doc/source/whatsnew/v2.1.0.rst

@@ -374,12 +374,12 @@ Period
 ^^^^^^
 - :meth:`PeriodIndex.map` with ``na_action="ignore"`` now works as expected (:issue:`51644`)
 - Bug in :class:`PeriodDtype` constructor failing to raise ``TypeError`` when no argument is passed or when ``None`` is passed (:issue:`27388`)
+- Bug in :class:`PeriodDtype` constructor incorrectly returning the same ``normalize`` for different :class:`DateOffset` ``freq`` inputs (:issue:`24121`)
 - Bug in :class:`PeriodDtype` constructor raising ``ValueError`` instead of ``TypeError`` when an invalid type is passed (:issue:`51790`)
 - Bug in :func:`read_csv` not processing empty strings as a null value, with ``engine="pyarrow"`` (:issue:`52087`)
 - Bug in :func:`read_csv` returning ``object`` dtype columns instead of ``float64`` dtype columns with ``engine="pyarrow"`` for columns that are all null with ``engine="pyarrow"`` (:issue:`52087`)
 - Bug in :meth:`arrays.PeriodArray.map` and :meth:`PeriodIndex.map`, where the supplied callable operated array-wise instead of element-wise (:issue:`51977`)
 - Bug in incorrectly allowing construction of :class:`Period` or :class:`PeriodDtype` with :class:`CustomBusinessDay` freq; use :class:`BusinessDay` instead (:issue:`52534`)
--
 
 Plotting
 ^^^^^^^^

pandas/core/dtypes/dtypes.py

@@ -899,7 +899,7 @@ class PeriodDtype(PeriodDtypeBase, PandasExtensionDtype):
     num = 102
     _metadata = ("freq",)
     _match = re.compile(r"(P|p)eriod\[(?P<freq>.+)\]")
-    _cache_dtypes: dict[str_type, PandasExtensionDtype] = {}
+    _cache_dtypes: dict[int, PandasExtensionDtype] = {}
     __hash__ = PeriodDtypeBase.__hash__
     _freq: BaseOffset
 
@@ -916,12 +916,12 @@ def __new__(cls, freq):
             freq = cls._parse_dtype_strict(freq)
 
         try:
-            return cls._cache_dtypes[freq.freqstr]
+            return cls._cache_dtypes[hash(freq)]
         except KeyError:
             dtype_code = freq._period_dtype_code
             u = PeriodDtypeBase.__new__(cls, dtype_code, freq.n)
             u._freq = freq
-            cls._cache_dtypes[freq.freqstr] = u
+            cls._cache_dtypes[hash(freq)] = u
             return u
 
     def __reduce__(self):

pandas/tests/arrays/test_period.py

@@ -22,6 +22,15 @@ def test_registered():
     assert result == expected
 
 
+def test_perioddtype_caching_dateoffset_normalize():
+    # GH 24121
+    per_d = PeriodDtype(pd.offsets.YearEnd(normalize=True))
+    assert per_d.freq.normalize
+
+    per_d2 = PeriodDtype(pd.offsets.YearEnd(normalize=False))
+    assert not per_d2.freq.normalize
+
+
 # ----------------------------------------------------------------------------
 # period_array