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Homework answers / question archive / This problem asks you to analyze the IS-LM model algebraically
This problem asks you to analyze the IS-LM model algebraically. Suppose consump- tion is a linear function of disposable income: C(Y −T)=a+b(Y −T), where a > 0 and 0 < b < 1. Suppose also that investment is linear function of the interest rate: where c > 0 and d > 0. I(r) = c − dr,
(a) Solve for Y as a function of r, the exogenous variables G and T, and the model’s parameters a, b, c, and d. [3]
(b) How does the slope of the IS curve depend on the parameter d, the interest rate sensitivity of investment? Refer to your answer to part (a), and explain the intuition. [5]
(c) Which will cause a bigger horizontal shift in the IS curve, a $100 tax cut or a $100 increase in government spending? Refer to your answer to part (a), and explain the intuition. [5]
(d) Suppose that demand for real money balances is a linear function of income and the interest rate: L(r,Y)=eY −fr. Solve for r as a function of Y , M, and P and the parameters e and f. [3]
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