In this exercise, you will derive how a change in the price of vaccines changes the steady-state infected population, I∗, in an SIR model – discussed in Section 21. 2 – in which the demand for vaccine is affected by the size of the infected population.

a. Recall the formula in the SIR reflecting the size of the susceptible population in steady state (please see Section 21. 2 for the description of the notation): Take the derivative of equation (21.14) with respect to p.

b. Recall the equation for the steady state-population of the susceptible group S∗ in equation (21.8). Does it depend on the price of vaccines p?

c. Using this fact about dS∗/dp that you derived in the last question, simplify the expression you derived in the first part of this question.

d. Now solve for dI∗/dp. When the prevalence elasticity of demand for the vaccine dv/dI∗ is high, is the the steady-state size of the infected population I∗ more or less affected by changes in the vaccine price, p, compared to when dv/dI∗ is low?

Transcribed Image Text:

dS* dt -=hp-BI-SV₁-S* - has* = 0 (21.14)