Monetary Economics (Basic) 2023
Problem set n° 1 (Continuation)
(a) Consider the model as discussed in class where all is the same except that
𝑐2𝑡+1
𝑈(𝑐1𝑡 , 𝑐2𝑡+1 ) = 𝑙𝑜𝑔𝑐1𝑡 +
1+𝜃
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
𝑈(𝑐1𝑡 , 𝑐2𝑡+1 ) = 𝑐1𝑡 +
𝑙𝑜𝑔𝑐2𝑡+1
1+𝜃
(b) Consider again the models in (a), now with an increasing money supply, which at each date
𝑡 = 1,2, ..is given by 𝐻𝑡+1 = 𝐻𝑡 (1 + ℎ) where ℎ > 0 is the growth rate of money supply. Find
the equilibrium price and consumption level.