df2['new'] = np.where(df2[df2.first_id.isin(df1.id.values)], 1, 0)

df1 = pd.DataFrame(np.random.randint(0,5,size=(100, 1)), columns=list('A')) # random 1 column df
df2 = pd.DataFrame(np.random.randint(0,5,size=(100, 1)), columns=list('B')) # random 1 column df
df2["new"] = df2.apply(lambda row: 1 if row[0] == df1["A"][row.name] else 0, axis = 1) # lambda function to check if they match. row.name gets the index
df2

In [387]: df1
Out[387]:
   id
0   1
1   2
2   3
3   4
4   5

In [388]: df2
Out[388]:
   first_id
0         7
1         6
2         5
3         1
4         3

In [389]: df2['new'] = df2.first_id.isin(df1.id).astype(np.int8)

In [390]: df2
Out[390]:
   first_id  new
0         7    0
1         6    0
2         5    1
3         1    1
4         3    1