The problem: the owner of my WordPress files did not match the users under which Apache and MySQL were executing. The owner of my WordPress files was “ThatMan”; Apache and MySQL were executing under the users “www” and “mysql”, respectively.
The solution: In MAMP, change the setting entitled “Run Apache/MySQL server as user”. Under MAMP Version 2.0.5., find this setting in the Main Window / Server button / General button.