Consider an overlapping generations model with the following characteristics. The economy has a constant population: N = 100 agents in each generation. Each agent is endowed with 30 units of time when young and nothing when old. A young agent divides his time between leisure and work, one unit of time spent on work produces one unit of current period good. This good is nondurable and consumed only by the old agents in current period, so the young agents sell their output on the market to the old agents for money. In period 1, the initial old collectively own a total of 1000 units of at money, M0 = 1000. In every period, starting from period 1, the central bank increases money supply by 50%, i.e., Mt = 1:5Mt1, and distributes equally the newly printed money among the old agents as a lump-sum subsidy. Preferences of all future generations (those who live for two periods) are such that at the equilibrium, each individual wishes to spend half of the time in leisure and work half of time when young and sell his output for money for old-age consumption. The equilibrium allocation is stationary over time. Write down the market-clearing condition for an arbitrary date t. Find the real rate of return of at money at the monetary equilibrium. What is the gross rate of in ation?