Problem #1 Imagine that in a given economy productivity is equal to a. and a worker who works L hours produces y = 3L units of output. Assume that labor in- come is taxed at rate T.Furthermore, assume that preferences of consumers are represented with 1 UK}, L) = C 2L2 + 2022. i) What is the deadweight burden in this economy? ii) What is the amount of revenue collected by the government relative to the deadweight burden? iii) Assume that a = 2. Is there a tax rate that allows the government to collect G' = 1 in revenue? iv) Now assume that the interest rate is equal to 0, the economy lasts for two periods, that a = 4, the government plans to collect 01 = 4 in the rst period and G2 = 0 in the second period. Furthermore, assume that the price of consumption is equal to 1 and the preferences are represented with 1 2 1 2 U=01L1+02 5L2. What is the total (the sum from both periods) value of the deadweight burden if the government balances its budget on a period by period basis? v) Continue with the assumptions of the previous period. Imagine that the government chooses to follow the optimal policy. What is the total value of the deadweight burden in this case