Suppose that at a given month the Fed conducts asset purchase in the open market (QE) of total vlue $50 bn, of which $30 bn are net purchases of Treasury bonds and $ 20 bn are net purchases of mortgage-backed securities (MBS). Suppose that the Fed purchases $40 bn of assets from commercial banks and the remaining $10bn from the non-banking private sector. During that period, lending to private sector by commercial banks increased by $60 bn and the Treasury General Account (TGA) increased by $440 bn as a result of net issuance of Treasury bonds by the US Treasury.From these $440 bn of net Treasury bond issuance, $200 bn is covered by the non-banking private sector and the remaining $240 bn by commercial banks. Answer the following:

a) Explain any changes in deposits that the private sector holds with commercial banks. Then explain any changes in reserve balances that commercial banks hold with the Fed. Please calculate the above changes by adding contributions of financial transactions to aggregate changes, without resorting to aggregate balance - sheet qualities, which you may use solely to verify your prior answer.