7. Consider the model of demand deposit banking where individuals live for three periods. Each individual is endowed with y units of the consumption good when young and nothing in the other two periods of life. No one consumes when young. Everyone wants to consume in one of the next two periods of life, depending on their types. With a probability 0.5, an individual wants to consume in the second period of life, which we label as early consumers. With a probability 0.5, an individual wants to consume in the third period of life which we label as late consumers. No one knows his type when young. In the beginning of the second period, an individual learns his type. The type of each individual is not observed by anyone else. Individuals have access to two assets: storage and capital. Storage pays a gross rate of return 1 over one period. Capital produces X (X > 1) goods for each good invested, but only after two periods of its creation. Capital cannot be sold early. That is, the early liquidation value of capital is 0. (a) Write down the budget constraints faced by an individual in each period of life without banks. When banks exist, write down the consumption allocation that an early consumer and a late consumer can achieve. Show how the existence of banks helps improve the welfare of individuals. (5 marks) (b) Describe how government deposit insurance helps prevent bank failures. List one potential problem associated with providing government deposit insurance