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Math Help - Aggregate demand - aggregate supply model

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    Nas
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    Aggregate demand - aggregate supply model

    Hi, I've been having problems with these questions, please help.

    1. The Aggregate Demand - Aggregate Supply Model

    An aggregate demand - aggregate supply model can be written as comprising two equilibrium conditions

    Y= C(Y-T) + I(r) + G and M/P= L(Y,r)



    The first equation states that the aggregate supply in the goods market is equal to aggregate demand. It is implied that consumption is determined by the function C(Y-T) and investment by the function I(r).

    The second equation states that the supply of real balances, nominal money supply M divided by the price level P, equals the demand for liquidity given by the function L(Y,r)

    In addition, the model includes an aggregate supply curve



    P= PE +g(Y-YF)


    where PE is the expected price level and YF the full-employment output.

    The model has three endogenous variables, Y, r and P. The remaining variables T, G, M, PE and YF are taken to be exogenous.

    (a) Find the government expenditure multiplier, an expression for the change in the equilibrium national income due to a change in government expenditure only.

    (b) Find the balanced-budget multiplier, an expression for the change in the equilibrium national income due to an equal change in government expenditure and taxes.


    2. The discriminating monopolist

    Consider a firm that sells in two separate markets. The inverse demand functions in the two markets are

    P1 = a1 -b1.q1 and P2 = a2 -b2.q2

    and



    and total cost is proportional to the total production
    c(q) = a.(q1 +q2)



    (a) Find the optimal (profit maximising) values of q1 and q2

    (b) State the sufficient second order conditions for these optimal values to maximise profits.

    (c) Explain the conditions the parameters must satisfy for the second order conditions to be satisfied.
    Thanks Nas
    Last edited by mr fantastic; April 27th 2010 at 05:07 AM. Reason: Re-titled.
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