Suppose planned expenditure in the goods market be given by AE = E(Y, i - ne, G, T) with 0 0, ET 0 where M is the quantity of money, P is the price level and L(.) is the demand for real balances. a. Derive di/dM and dY/dM for a given value of P. b. The derivation of the LM curve assumes that M is exogenous. Suppose instead that the monetary authorities has some target interest rate i and it adjusts M to keep i always equal to T. With this policy, what is the slope of the LM curve? What will be the slope of the AD curve? c. How do equal increases in G and T affect the position of the IS curve? Specifically, what is the effect on Y for a given level of i? d. How do equal increases in G and T affect the position of the AD curve? Specifically, what is the effect on Y for a given level of P? e. Suppose that tax revenues, 7, instead of being exogenous are a function of income: T= T(Y), T'(Y) > 0. Find how an increase in T'(Y) affects the following: The slope of the IS curve. 11. The effects of changes in G and M on Y for a given P