Consider the following model of demand for insurance (identical to that studied in class). Risk-averse individuals maximize expected utility of wealth where wealth is random due to a loss L, that occurs with probability π. Insurance carries a premium, P = p · I, where p is the price per dollar of insurance and I is the dollar amount of insurance purchased. Full insurance implies I = L while a deductible implies I < L. Please answer the following: (a) It is assumed that insurance companies operate in a perfectly competitive market. What does that imply for their profits? What does that imply for the value of the insurance premium P? (b) Let wealth in the no-loss state be denoted W1 while wealth in the loss state is denoted W2. What is the rate at which agents can transfer wealth between the loss and the no-loss state via the purchase of insurance? (c) What is the slope of individuals’ indifference curves, i.e. what is the rate at which agents are willing to transfer wealth between the loss and the no-loss state? (Yet another way to put the same question: What is the individuals’ marginal rate of substitution between wealth in the two states of the world?) (d) Show that, in this scenario, individuals will choose to purchase full insurance against the loss. (e) Illustrate your results for parts (a)-(d) in a graph in the (W1, W2)-space.