please answer the attached questions

Consider an economy where demand for real money balances is (M / P)D = eY fi + e . The variable 6 represents the effect of any special factors, other than real income or the nominal interest rate, that might affect money demand. The real interest rate is r = i E' . The money supply M S is determined by the central bank. 1) Derive an equation that gives (M / P)D as a function of Y, EJZ', r and e . In this equation, (M / P)D should be alone on the lefthand side. 2) Starting from your answer to 1), do some algebra and derive an equation that gives r as a function of (M / P)D , Y, E 75' and E. This is the "equation of the money demand curve." 3) Draw a money supply/demand graph with r on the vertical axis and M/P on the horizontal axis. Show what happens if the price level increases from P0 to P1 (nothing else changes). Label the "before' real interest rate as r0 and the "after" real interest rate as r1 . 4) a) Draw a money supply/demand graph that shows what happens in an economy if the price level increases by exactly ten percent and, at exactly the same time, the central bank increases the money supply by exactly ten percent. Label the "before" real interest rate as 1'0 and the "after" real interest rate as r] . 4) continued b) Consider your answer to a). In the situation you drew there, was the central bank buying stuff, selling stuff, or neither? 5) Draw a money supply/demand graph that shows what happens in an economy if there is a special factor that tends to increase money demand, that is, if E increases from ED to El , while nothing else changes. Label the "before" real interest rate as r0 and the "after" real interest rate as r] . 6) Suppose the central bank adjusts the money supply every single day so as to keep r equal to a predetermined value r, (for example, 2 percent). a) Draw a money supply/demand graph that shows what would happen if there is a special factor that tends to increase money demand, that is, 6 increases from ED to 1 , while the central bank always keeps r equal to the predetermined value 1'], . Mark rT on the graph. Assume Y, E73 and P do not change