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Assume a closed economy without Government. However, there exists a financial sector that creates an array...

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Advance Math

Assume a closed economy without Government. However, thereexists a financial sector that creates an array of financial assetson which both households and firms invest.

Let ? denote the average earnings from these financial assets.The consumption expenditure of the households is influenced bytheir wage income and the financial income and is given by ? = ?(?,?); ?? > 0, ?? > 0, where ??, ?? are partial derivatives ofconsumption with respect to income ? and financial earnings ?respectively. Similarly, the real investment expenditure of firmsis given by ? = ?(?, ?); ?? > 0, ?? < 0, where ??, ?? are thepartial derivatives of the real investment with respect to incomeand financial earnings. Using either the Keynesian cross model orthe Multiplier analysis, answer the following questions.

(i) Derive the relationship between output ? and financialearnings ?, and examine the analytical conditions under which therelationship is positive ( ?? ?? > 0) and negative ( ?? ?? <0).

(ii) Describe why the scenario where the expansion in outputdriven by the rise in financial earnings, i.e. when ?? ?? > 0,could make the economy unstable and vulnerable to crisis?

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