Monetary Economics (Basic) 2023 Problem set n° 1 (Continuation) (a) Consider the model as discussed in class where all is the same except that ๐2๐ก+1 ๐(๐1๐ก , ๐2๐ก+1 ) = ๐๐๐๐1๐ก + 1+๐ Find the optimum level of consumption in the two periods as well as money and equilibrium price behaviour. Repeat the exercise with the following lifetime utility function ๐(๐1๐ก , ๐2๐ก+1 ) = ๐1๐ก + ๐๐๐๐2๐ก+1 1+๐ (b) Consider again the models in (a), now with an increasing money supply, which at each date ๐ก = 1,2, ..is given by ๐ป๐ก+1 = ๐ป๐ก (1 + โ) where โ > 0 is the growth rate of money supply. Find the equilibrium price and consumption level.