Question

1 Suppose that the price of outpatient healthcare is $1, and we go on 10 inpatient visits. When the price of outpatient healthcare increases to $2, we go on 15 inpatient visits. What is the elasticity of inpatient care with respect to the price of outpatient care?

2 Suppose that the price of inpatient healthcare is $5, and we go on 10 outpatient doctor's visits. The price of inpatient healthcare increases to $7.50, and we go on 8 outpatient doctor's visits. What is the elasticity of outpatient healthcare with respect to the price of inpatient healthcare?

3 Suppose that for the first 3 months, you have the flu, where the utility from your health is 0.5. The next 6 months, you are in perfect health, and the utility from your health is 1. The last 3 months, you have allergies, where the utility from your health is 0.8. What is the value of the QALY? Answer to THREE decimal points.

Answer 1

1)  

elasticity of inpatient care with respect to the price of outpatient care = ( change in number of inpatient customers in % ) / ( change in price of outpatient care in % )

change in number of inpatient customers in % = ( Q₂ - Q₁ ) / Q₁

change in number of inpatient customers in % = ( 15 - 10 ) / 10 = 50 %

change in price of outpatient care in % = ( P₂ - P₁ ) / P₁

change in price of outpatient care in % = ( 2 - 1 ) / 1 = 100 %

e = 50 % / 100 %

=> e = 0.5

2)

elasticity of outpatient care with respect to the price of inpatient care = ( change in number of outpatient customers in % ) / ( change in price of inpatient care in % )

change in number of outpatient customers in % = ( Q₂ - Q₁ ) / Q₁

change in number of outpatient customers in % = ( 8 - 10 ) / 10 = - 20 %

change in price of inpatient care in % = ( P₂ - P₁ ) / P₁

change in price of inpatient care in % = ( 7.5 - 5 ) / 5 = 50 %

e = - 20 % / 50 %

=> e = - 0.4 ( -ve sign indicates that the number of outpatient customers decreases if price of inpatient care is increased )

3)

Utility in the first 3 months ( 25% of the year ) = 0.5

Utility for the next 6 months ( 50 % of the year ) = 1

Utlity for the last 3 months ( 25 % of the year ) = 0.8

QALY score = X_i U_i

X_i = percentage of time in years of time period i

U_i = Utility for the person in the i^th time period

=> QALY score = ( 0.25*0.5 ) + ( 0.5*1 ) + ( 0.25*0.8 )

=> QALY score = 0.125 + 0.5 + 0.2

=> QALY score = 0.825

Therefore, the QALY score for the person will be 0.825.