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Health Care: Number of Healthy Days vs. Price of Treatments

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Use the information below to determine the relationship between price and health status in this model. In other words, solve for D and for P, and set up two equations: one showing the value of D in terms of P; and one showing the value of P in terms of D. Once you have determined the two equations, provide an interpretation of each equation.

A model of the determinants of health combines three economic variables and two economic relationships.

For instance, the three economic variables are:

the amount a patient pays for a visit to a physiotherapist (P);
the number of times the patient visits the physiotherapist (V); and
the length of time it takes the patient to recover from a rotator cuff (shoulder) injury (D) (max. = 365 days).

The two economic relationships are:

the number of visits (V) = 18 - $0.09 (P).

In other words, if the price is zero, the patient will make 18 visits in order to receive treatment for this injury. If the price is $200, the patient will make zero visits.

the number of days to recover (365 - D).

In this case, the number of healthy days (D) in the next year will be 180 + 5V. If the number of visits is zero, the patient will have 180 healthy days and it will take 185 (365 - 180) days to recover from the rotator cuff injury. If the number of visits is 18, the patient will have 270 [180 + 5(18)] healthy days, and the time to recover from the injury will be 95 days (365 - 270).

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Solution Summary

How to substitute equations to solve for healthy days and price of treatments in terms of each other.

Solution provided by:
Robert Reinhart, MBA
Education
  • MBA, Merage School of Business, Univ of Cal, Irvine
  • BA, Univ of Cal, Irvine
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