Then explain how inspiration and expiration work.  What causes the lung to inflate with air?  Why do they deflate?  What part of the process requires a "muscle contraction" of the diaphragm?

The external intercostals and diaphragm and the diagram contracts to bring about inspiration. The contraction of the external intercostal leads to the elevation of the ribs and sternum which increases the dimensions of the thoracic external cavity. This all lower s the pressure in the lungs and lets air move into the lungs.

Expiration is the relaxation of the diaphragm and intercostal muscles. This returns the thoracic cavity to its resting position including the diaphragm, ribs and sternum. This increases the pressure in the lungs and then the air is exhaled.