Consider a two-period overlapping generation model economy where agents work when young and retire when old. Young agents supply inelastically labour to the competitive firm who produces the only good in the economy using capital and labour through a Cobb- Douglas production function. In this economy there is no population growth nor growth in the efficiency per worker. Thus, the production function in terms of total capital (K) and total young labour (L) is given by Y = KaL-a Agents obtain utility from consuming when young and old as well from public goods provided when young and old. In particular, preferences are given by 1-0 1-0 C C u(C, C,9) = 1 + = 0 + 1 + 192-0 g) 1-0 1-0 1-o Suppose the government taxes young and old proceeds towards the public goods 9 and 9 consumption at a rate and uses the When answering the following questions make sure you provide all the relevant explanations, derivations and steps to obtain full marks. 1. Write down the individual's utility maximisation problem and explain each component, including budget constraints. 2. Write the firm's profit maximisation problem and explain each component. 3. Derive the optimal savings and the first order conditions for the firms profit maximising problem in terms of per capita capital. 4. Write down the market clearing condition corresponding to the credit market. 5. Derive the per capita capital accumulation and find the corresponding steady state value. 6. What is the effect of consumption taxes on the per capita capital steady state?