Nick vs Scott on HPE Hypothetical: Balance Sheets

Below are the balance sheets prior to the central bank changing the quantity of reserves to Ms1. As an aside, note that I think it's fair to claim that Ms + A + E - L - F - G = 0, but that has no bearing on what I'm trying to demonstrate. Also if we assume that the commercial bank's only other assets, aside from reserves, are loans, and that E only means financial assets, then we can simplify as follows:

A = L
Ms + E - F - G = 0

For example E might be bonds issued by the commercial banks. G might be the total number of bonds issued by the commercial bank (G - E of which are owned by the central bank), and F might represent bonds issued by the non-bank private sector, all of which are owned by the central bank.

Here's the balance sheets:

Central Bank

Assets	Liabilities
Ms0 assets	Ms0 reserves
Total Assets	Total Liabilities
Ms0	Ms0
Negative Equity	Equity
0	0

Sole Commercial Bank

Assets	Liabilities
Ms0 reserves	D0 deposits
A0 other assets (e.g. loans)	G0 other liabilities
Total Assets	Total Liabilities
Ms0 + A0	D0 + G0
Negative Equity	Equity
--------------------------	Ms0 + A0 - D0 - G0

Non-bank Private Sector Financials

Assets	Liabilities
D0 deposits	L0 loans at commercial bank
E0 other assets	F0 other liabilities
Total Assets	Total Liabilities
D0 + E0	L0 + F0
Negative Equity	Equity
------------------	D0 + E0 - L0 - F0

Below I show the balance sheets immediately after the central bank conducts OMOs thus changing the reserve level to Ms1. Note that

B + C = Ms0 - Ms1

Note that if we assume Ms0 > Ms1 (i.e. that the central bank sold assets), then B represents the number of assets purchased by the commercial bank and C represents the assets purchased by the non-bank private sector. Note that nobody's equity changed:

Central Bank

Assets	Liabilities
Ms1 assets	Ms1 reserves
Total Assets	Total Liabilities
Ms1	Ms1
Negative Equity	Equity
0	0

Sole Commercial Bank

Assets	Liabilities
Ms1 reserves	D0 - C deposits
A0 + B other assets (e.g. loans)	G0 other liabilities
Total Assets	Total Liabilities
Ms1 + A0 + B	D0 - C - G0
Negative Equity	Equity
------------------------------	Ms1 + A0 + B - D0 + C + G0 = Ms0 + A0 - D0 - G0

Non-bank Private Sector Financials

Assets	Liabilities
D0 - C deposits	L0 loans at commercial bank
E0 + C other assets	F0 other liabilities
Total Assets	Total Liabilities
D0 + E0	L0 + F0
Negative Equity	Equity
------------------	D0 + E0 - L0 - F0

Below I look at the balance sheets after the steady state average price level (P) reaches a new equilibrium (P1). Note that I've abandoned the variables B and C because there's no telling what will happen to loans vs deposits as the economy reaches a new equilibrium. Instead I fold whatever changes happen into the new variables A1, D1, E1, F1, G1 and L1. The result is the new set of balance sheets looks exactly like the first set, except the subscript "0" has been replaced with "1.":

Central Bank

Assets	Liabilities
Ms1 assets	Ms1 reserves
Total Assets	Total Liabilities
Ms1	Ms1
Negative Equity	Equity
0	0

Sole Commercial Bank

Assets	Liabilities
Ms1 reserves	D1 deposits
A1 other assets (e.g. loans)	G1 other liabilities
Total Assets	Total Liabilities
Ms1 + A1	D1+ G1
Negative Equity	Equity
------------------------------	Ms1 + A1 - D1- G1

Non-bank Private Sector Financials

Assets	Liabilities
D1 deposits	L1 loans at commercial bank
E1 other assets	F1 other liabilities
Total Assets	Total Liabilities
D1 + E1	L1 + F1
Negative Equity	Equity
------------------	D1 + E1 - L1 - F1