Suppose that consumer spending initially rises by $$6$ billion for every $1$ percent rise in household wealth and that investment spending initially rises by $$25$ billion for every $1$ percentage point fall in the real interest rate. Also assume that the economy's multiplier is $3.$

a$)$ If household wealth falls by $5$ percent because of declining house values, how will aggregate demand initially shift, in which direction and by how much?

b$)$ If the interest rate falls by $2$ percentage points, how will aggregate demand initially shift, in what direction and by how much?

c$)$ If both changes happen at the same time, over the long run, what would be the net effect on aggregate demand and GDP$?$