Problem 5 Let t€ (0.1) be a labour tax rate paid by consumer, so the labour income is now (1-t)wL. Assume that production function is Cobb-Douglas Y = AKL with A = 1, K = 1 due to proper normalization. Preferences of agent are given by: U(C.L)=aC- 1. Derive labour supply function. 2. Derive labour demand function. 3. Find equilibrium wage rate w* and equilibrium labour L*. 4. Write tax revenue as a function of tax rate. Find optimal tax rate and sketch the graph for revenue.