Our end-goal with this question is to derive the expected inflation rate is for the economy described below.

We'll start with the Money Supply and Money Demand curves.

M^S = 1000

M^D = P*L(Y₊,i_-), where L(Y,i) is known as the Liquidity function

The description above says that, all else equal, money demand:

changes one-to-one with price level (if the price increases by 10% then, all else equal, a person requires 10% more money)

is positively correlated with real GDP, Y (though not necessarily one-to-one)

is inversely correlated with the nominal interest rate

Suppose the price level in the economy is 2, real GDP is 1250 and Liquidity function is described as L(Y,i) = (Y/10)^1/3/i² (careful of the brackets!)