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Table 2 Function expressions of variables

From: Reducing the quality risk of elderly care services in government procurement from market-oriented private providers through ex ante policy design: lessons from the principal-agent theory analysis

Expression and definition Predicated model assumption
x follows a linear uncertainty distribution √Assumption (1)
\( y(x)=\left\{\begin{array}{l}1,0<x<1\\ {}0,\begin{array}{c}\end{array} others\end{array}\right. \) √Assumption (2)
U(λ, q(x)) = λ ln q(x) √Assumption (3)
w(σ, ε, x) = σeεx2 √Assumption (4)
C(θ, q(x), x) = θq(x)/(x + 3) √Assumption (5)