Consider a closed economy (NX = 0) and assume the following functionswhere I is autonomous investment expenditure; ir is the real interest rate, b > 0; TR denotes transfers, which are assumed to be exogenous; and TA denotes taxes, which are given by TA = t , Y, where t is the tax rate on income.

a. Derive the aggregate demand function.

b. Derive the equation for the IS curve.

c. What is the slope of the IS curve?

d. Discuss how the slope of the IS curve is affected by b, t, and mpc.

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C= a + mpc x (Y+TR-TA) 1= I- bi, G=G