MEF Property Allways Returns Zero

Source code

I have a simple business object in the BusinessObjects.dll file:

namespace BusinessObjects
{
    public class MyClass
    {
        public MyClass()
        {
            DateTime = DateTime.Now;
        }

        public DateTime DateTime { get; set; }
    }
}

In my SharedUI.dll I have this class "Context Provider", which I use to conduct the referee for the currently selected MyClass - remember that this is a simple example:) ...

namespace SharedUI
{
    public class AppContext
    {
        [Export]
        public MyClass SelectedMyClass { get; private set; }

        public void SetupContext(MyClass myClass)
        {
            SelectedMyClass = myClass;
        }

        public static AppContext Context
        {
            get
            {
                if (context == null)
                {
                    context = new AppContext();
                }
                return context;
            }
        }

        private static AppContext context;
    }
}

My MefTest.exe has this class:

namespace MefTest
{
    public class Program
    {
        [Import]
        public MyClass MyClass { get; set; }

        private void Compose()
        {
            var ventSystem = new MyClass();
            AppContext.Context.SetupContext(ventSystem);

            var executingAssembly = new AssemblyCatalog(Assembly.GetExecutingAssembly());
            var contextAssembly = new AssemblyCatalog(Assembly.LoadFile(string.Format(@"{0}\SharedUI.dll", Environment.CurrentDirectory)));
            var catalog = new AggregateCatalog(executingAssembly, contextAssembly);

            var container = new CompositionContainer(catalog);

            container.ComposeParts(this);
        }

        private void Run()
        {
            Compose();

            // MyClass is always null in the next line?
            Console.WriteLine(MyClass.DateTime.ToString());

            Console.ReadKey();
        }

        private static void Main(string[] args)
        {
            var p = new Program();
            p.Run();
        }
    }
}

I am new to MEF, so please bear with me :)

UPDATED Source code with suggestions from Daniel Plaisted

MyClass source is the same ...

SharedUI.dll now looks like this:

namespace SharedUI
{
    [Export]
    public class AppContext
    {
        [Export(typeof(MyClass))]
        public MyClass SelectedMyClass { get; private set; }

        public void SetupContext(MyClass myClass)
        {
            SelectedMyClass = myClass;
        }
    }
}

MefTest.exe now looks like this:

namespace MefTest
{
    public class Program
    {
        [Import]
        public MyClass MyClass { get; set; }

        [Import]
        public AppContext AppContext { get; set; }

        private void Compose()
        {
            var executingAssembly = new AssemblyCatalog(Assembly.GetExecutingAssembly());
            var contextAssembly = new AssemblyCatalog(Assembly.LoadFile(string.Format(@"{0}\SharedUI.dll", Environment.CurrentDirectory)));
            var catalog = new AggregateCatalog(executingAssembly, contextAssembly);

            var container = new CompositionContainer(catalog);

            container.ComposeParts(this);

            var myClass = new MyClass();
            AppContext.SetupContext(myClass);
        }

        private void Run()
        {
            Compose();

            // AppContext.SelectedMyClass is NOT null in the next line... which is good I guess :)
            Console.WriteLine(AppContext.SelectedMyClass.DateTime.ToString());

            // MyClass is always null in the next line?
            Console.WriteLine(MyClass.DateTime.ToString());

            Console.ReadKey();
        }

        private static void Main(string[] args)
        {
            var p = new Program();
            p.Run();
        }
    }
}

What am I doing wrong since I cannot get it to work?