Consider an economy in which there are 200 workers. Three-fourths of the workers are endowed with 100 units of the consumption good when young and nothing when old. The remaining workers are endowed with 20 units of the consumption good when young and nothing when old. Each worker saves 50 percent of their endowment when young. Let the gross real return on capital be 1.25. There are 50 entrepreneurs in the economy. Each entrepreneur is endowed with 50 units of the consumption good when young and nothing when old. Entrepreneurs only want to consume when they are old. Let the stock of money be constant over time. Assume that each worker uses 20 goods to identify themself and make a withdrawal from a bank. At date , there a permanent increase in the return on capital to 1.3.
a. Compute GDP in period t.
b. Compute GDP in period t+1.
c. What are aggregate deposits in dates t and t+1?
d. For this model economy, what is the correlation, if any, between aggregate deposits and GDP over the two time periods?