Consider a risk-averse individual with initial wealth w0 and a Bernoulli utility function u(w) who must decide whether and for how much to insure his car. Assume the probability that he will not have an accident is . In the event of an accident, he incurs a loss of $L < w0 in damages. Suppose that insurance is available at an actuarially fair price, that is, one that yields insurance companies zero expected profits; denote the price of $1 worth of insurance coverage by p. Assume it costs nothing to run an insurance company. calculate the competitive equilibrium values of the following derivatives:

(i) dx/dp;

(ii) dx/dw₀