Suppose the central bank of a country has set a target inflation rate of 2%. The economy is currently in a recession, with output (real GDP) below potential GDP. The central bank wants to use monetary policy to stimulate the economy and close the output gap.

a) Suppose the money demand function in the economy is given by:
Md = 500 + 0.2Y - 100i

where Md is the demand for real money balances, Y is real GDP, and i is the nominal interest rate. If the central bank wants to increase real money balances by 2%, by how much should it increase the money supply?

b) Suppose the money supply increases by the amount calculated in part (a). Using the IS-LM model, show the impact of this monetary policy on the economy, including the interest rate, output, consumption, and investment.

c) If the central bank wanted to achieve the same increase in real money balances using an interest rate policy, what would be the required change in the nominal interest rate?

Show all your calculations and provide detailed explanations for each part of the question.

Note: Assume that the price level is constant and there is no government spending or taxes in the economy.