Say that the firm is attempting to calculate their maximum willingness to pay for fixed asset insurance. In this case, we'll consider insurance that covers machinery failure for a manufacturing firm.
Given the production function:
$q = x_1^{a_{1}}...x_n^{a_{n}}$
Where $x$ is a vector of production inputs, $a$ is a vector of production returns to each input, and $q$ is the units of production output. Suppose the machinery represents $x_1$. In the failure state, $x_1 = 0$, and therefore $q_f =0$. In the fully operational state, suppose $q_o = 20,000$.
Given the revenue function:
$R = pq$
Where $p$ is the price of the output unit and $q$ is the units of production output. Assume the cost function is not affected by the machinery failure. Assume the probabilty of machinery failure in a particular time step, $p_f$, equals .02. Therefore, the probability of a fully operational state, $p_o$, equals .98.
Assuming the unit price of output is $50, we calculate the expected value of Revenue:
$E(R) = p_f R_f + p_o R_o = p_f (pq_f) + p_o (pq_o) = .02(50 \times 0) + .98(50 \times 20,000) = \$980,000$
Assuming full insurance $-$ meaning that the insurer will pay the insuree the difference in outcome between failure and fully operational states $-$ the firm's maximum willingness to pay for the insurance premium is the difference between Revenue in the fully operational state and expected state. Therefore, the firm's maximum wllingness to pay for the machinery insurance is:
$R_o - E(R) = \$1,000,000 - \$980,000 = \$20,000$