A solve for y as a function of r the exogenous

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Exploring Microeconomics
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Chapter 17 / Exercise 1
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a. Solve for Y as a function of r, the exogenous variables G and T, and themodel’s parameters a, b, c, and b. How does the slope of the IS curve depend on the parameter d, the interestsensitivity of investment? Refer to your answer to part (a), and explain the intuition.c. Which will cause a bigger horizontal shift in the IS curve, a $100 tax cut or ad.
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Chapter 17 / Exercise 1
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$100 increase in government spending? Refer to your answer to part (a), and explainthe intuition. Now suppose demand for real money balances is a linear function of
fr,
d. Solve for r as a function of Y, M, and P and the parameters e e. Using your answer to part (d), determine whether the LM curve is steeper forlarge or small values of f, and explain the intuition.f. How does the size of the shift in the LM curve resulting from a $100 increase inM depend oni. the value of the parameter e, the income sensitivity of money demand?ii. the value of the parameter f, the interest sensitivity of money demand?g. Use your answers to parts (a) and (d) to derive an expression for the aggregatedemand curve. Your expression should show Y as a function of P; of exogenous policyvariables M, G, and T; and of the model’s parameters. This expressionshould not contain rh. Use your answer to part (g) to prove that the aggregate demand curve has anegative slope. i. Use your answer to part (g) to prove that increases in G and M, and decreases inT, shift the aggregate demand curve to the right. How does this result change if theparameter f, the interest sensitivity of money demand, equals zero? Explain theintuition for your result.and f..a) The goods market is in equilibrium when output is equal to planned expenditure,or Y = PE. Starting with this equilibrium condition, and making the substitutionsfrom the information given in the problem, results in the following expression forequilibrium output Y: Y=C+I+GY = C(Y-T) + I(r) + G Y = a + b(Y-T) + c -dr + G (1 -b)Y =a-bT +c-dr+ GY=abT+cdr+G1bb)The slope of the IS curve is measured as (Δr )/ΔYFrom the equation in part (a), the slope of the IS curve can be found as
follows :(Δr )/ΔY=1/((ΔY/Δr))=1/(-(d /(1-b)) )=-(1-b)/d Mathematically, as the parameter d becomes a larger number, the slope becomes asmaller number in absolute value terms and the IS curve becomes flatter. Intuitively , if the parameter d is a larger number, then investment is moreresponsive to changes in the interest rate . Any given decrease in the interest rate willcause a larger increase in investment and, via the multiplier effect and a largerincrease in equilibrium output Y. This makes the IS curve flatterc) A $100 increase in government spending will cause a larger horizontal shift in theIS curve than a $100 tax cut.From the equation for equilibrium output in part (a), we note that the impact of the taxcut depends on the marginal propensity to consume , as given by the parameter b. Ifthe MPC is 0. 75, for example, then a $100 tax cut will shift the IS curve by only $75.

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