Most systems of medical insurance substantially lower the out-of-pocket costs consumers have to pay for additional units of medical services, eventually reducing to zero. How does this method of payment affect the consumption of medical services

The out of pocket cost to health insuree's is capped by the policy holder per the premiums paid by the insuree. The insurer, if it's an employer policy, can raise not only the cap maximum but also the premium each renewal period.
This is a two way deal. If the use of medical services increases by employees of the plan, at renewal time they can increase the cap/premium to ensure profit.
Use of medical services is dictated by the diagnosis of the physician. i.e. a cancer diagnosis in a three month period can reduce the cap to zero. Caps include all medical services - i.e. lab tests, treatments, hospitalizations, diagnostic tests and doctors fees.
The insuree who has a cap of say $3,000 or the insuree who has a cap of $10,000 would still get same medical services. Only difference, the insuree would pay, $7,000 more out of their money