This problem just needs a little explanation for each one.

A health insurance contract is characterized by its premium (r) and its payment in case of sickness (q). Individuals know their probability of becoming sick (p) and their utility only depends on their income (which equals 1H when healthy, 15 when sick -- Do not worry about the subscripts when you type your answers). 1. Given p, 1H and Is , what condition does 1' or q have to satisfy for the insurance contract to be full? (Explain and express it in a simple equation) 2. Given p, 1H and Is , what condition does r or q have to satisfy for the insurance contract to be actuarially fair? (Explain and express it in a simple equation) 3. Consider the figure below, corresponding to the market for health insurance in the Rothschild-Stiglitz model with asymmetric information for a country with two types of individuals: robust and frail. The current state of this insurance market is a separating equilibrium where contracts 01 and 03 are offered, as depicted in the gure below. In this separating equilibrium, what contract do the robust choose? Explain why no insurance firm offers contract 02. 4. Suppose the government of the country in this example wants to establish a new national pooling equilibrium. For this, the government starts offering a health insurance contract at point P aimed at robust and frail customers. Draw the indifference curve for the robust type that goes through contract P in the figure above. (You can hand draw your figure and take a picture or do it using Word or other software. You can also include in this figure what the question below asks. ) 5. The government still allows health insurance firms to offer other contracts if they want. Would health insurance firms want to offer any contract different than P in this case? If yes, indicate an example in the graph above. If no, explain why. 6. Is the government policy going to successfully sustain a pooling equilibrium like P? Explain.