Show with entries how the balance sheet will change when the Fed simultaneously engages in a$)$ a $$200$ billion quantitative easing with the purchase of $10-$year Treasuries and b$)$ a targeted $$200$ billion purchase of mortgage$-$backed securities versus $10-$year Treasuries.

Assets Liabilities

Foreign Exchange $500$ Bank cash $800$

$10$year government bonds $100$ Money in circulation $200$

$3$ month government bills $400$

Total $1000$ Total $1000$