Consider a one period model in which a representative agent maximises the utility function: U (c, 1) = Inc + 5lnl subject to the budget constraints: c = (1 t)w(1 1) + v where c is consumption and is the amount of leisure, they enjoy out of a total of one unit of time available, t is the tax on wage earnings which pays for v in government transfer payments. a) Solve for first order conditions of the representative agent. 2 marks b) Write down the market clearing condition (resource constraint) for the aggregate economy. 3 marks c) Solve for equilibrium consumption and labour choices. 10 marks d) Derive the equation that determines how much revenue the government will receive for a given rate of tax t. What is this relationship called? 5 marks e) Solve for the maximum amount of revenue the government can raise from this tax. Hint: the tax rate will be a fraction between 0 and 1. 10 marks f) In general, what explains the shape of the Laffer curve? 5 marks g) In this particular example, what are the contributions of the income and substitution effects? 5 marks