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The introduction of a visit fee is a counterproductive rationing device for health care services if it rations a component of overall health care services with a low own price elasticity of demand without rationing a substitute variable (visit intensity) with a higher cross elasticity of demand. Thus, the introduction of a visit fee may induce a sense of entitlement for further health care services per visit on the part of consumers, leading to an increase in overall health care expenditures.
The change in the demand for OP care in response to the change in price of IP care represents the cross elasticity of demand of OP care for IP care.
They define cross price elasticity as "the responsiveness of demand to changes in the price of another product is called the cross elasticity of demand." However, then they write the cross price elasticity formula as the percentage change in quantity demanded divided by the percentage change in the price of Good Y.
Rearranging equations (26)-(28) into elasticity form and assuming cross elasticity of demand is zero, we get the standard Ramsey result represented by equation (29).