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Solution: In Exercises 21 to 24, find the measure of the

College Algebra and Trigonometry | 7th Edition | ISBN: 9781439048603 | Authors: Richard N. Aufmann ISBN: 9781439048603 155

Solution for problem 24 Chapter 5

College Algebra and Trigonometry | 7th Edition

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College Algebra and Trigonometry | 7th Edition | ISBN: 9781439048603 | Authors: Richard N. Aufmann

College Algebra and Trigonometry | 7th Edition

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Problem 24

In Exercises 21 to 24, find the measure of the reference angle for the given angle . Assume is in standard position.

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ECON 3020 Notes for Week #13 11 April 2016 Deriving Aggregate Demand ● In late 2007 the Fed reduced the Federal Funds Rate (FFR) to almost 0% ○ FFR: the rate banks charge other banks for interbank loans ● The Fed can set the FFR at pretty much whatever they want and it is highly important for policy in the US ● The Fed decreases this rate by increasing liquidity through open market purchases and increases this rate by decreasing liquidity through open market sales ● The FFR is a nominal rate ● The Fed controls the real interest rate as follows e ○ r = i − π a ○ For the Fed to affect r, π must remain unchanged ○ In the short run, it is unlikely for prices to change much, so the Fed can affect r by changing i (the FFR) ○ In the long run, however, r is at the intersections of the S and I curves ● Relationships between the interest rates the Fed sets and the economy’s π rates ○ The monetary policy (MP ) curve represents this ○ r = r + λπ where λ is positive ○ ○ According to the MP curve, the Fed chooses to increase r with increases in π because they are following the Taylor principle ○ Taylor principle: named after John Taylor, says if π increases, central banks will increase r ○ If they did not raise r in times of high inflation then r would decrease causing Y to increase which causes π to increase in turn; this then becomes cyclical and leads to extreme inflation rates ● Automatic changes in r and autonomous changes in r ○ Automatic changes: Taylor driven changes as a result of changes in π; movements along the MP curve ○ Autonomous changes: when the Fed changes r, shifting the MP curve up or down ○ Real world example: ■ Up until the beginning of 2008, the Fed did not follow the MP curve, the reduced the FFR even as π increased ■ This was a downward shift of MP to MP ′ where r was decreased significantly; called an easing of monetary policy (the opposite is called a constriction of monetary policy) ■ The Fed did this because it predicted the real estate bubble bursting and other short­term economic failures and knew it would need to stimulate spending soon; this is seen when π began decreasing significantly in late 2008 ■ Why would the Fed increase r To slow down inflation if the economy was heating up too quickly ● Combining the IS curve and the MP curve we can derive the aggregate demand (AD) curve ● ● AD curve tells us levels of aggregate output based on levels of inflation for which the Fed has set a real interest rate 13 April 2016 Aggregate Demand (continued) ● The FFR that the sets must be higher than π in order for r to be higher when π is increasing ● The AD curve is negatively sloped because as π increases the Fed increases r, decreasing C , I , and NX, so Y decreases ● AD curve ○ Y = (C + I + G + NX − MPC ∙ T) ∙(1−MPC)−(1−MPC)∙ r and r = r + λπ ○ Then the AD curve is given by Y = (C + I + G + NX − MPC ∙ T) ∙ 1 − (c+d+x∙ r + λπ (1−MPC) (1−MPC) ● Movements along the AD curve are caused by changes in π ● Shifts of the AD curve are caused by changes in C, I, G, NX (all cause rightward shifts when increased), or T (causes leftward shifts when increased) ● ● In the above example, 1 represents an increase in G of $1 billion and 2 represents a decrease in T of the same amount ● When the Fed increases r, they are constricting, and thus the MP curve shifts upward; the economy will then function at a lower Y on the IS curve, leading to a shift in the AD curve so that this level of Y matches the respective levels of π for a given r on the MP curve ● If there is more money in the economy, AD curve shifts right; if there is less money in the economy, AD curve shifts left ● Not interested in quantity of money, but in real money balances ● Real money balances: the purchasing power of a given quantity of money ● Given by Md where M is money demanded and P is price level P M d ● According to Keynes the liquidity preference framework, L, is P = L(i, Y ) where money demanded divided by price level equals the liquidity preference framework as a function of nominal interest rate and output with a negative correlation to i and a positive correlation to Y ● ○ The demand for money increases as nominal interest rate decreases ○ The supply for money is set at any level by the Fed M ○ In the short run, the supply of real money balances is given by P 15 April 2016 How the Fed is Able to set the FFR ● Discovered through the liquidity preferences framework ● From Keynes perspective, the quantity of money is not important, but rather the purchasing power of money is; discussed through real money balances d ● As i increase, M decreases because bonds become more attractive d ● As Y increases, we will spend higher quantities of money so M increases ● As we have more money our wealth increases ● The Fed supplies money through open market transactions s Md M s ● The Fed chooses to set the M at a point such that when P = P (equilibrium is achieved), the desired i is given ● If the i was higher than the equilibrium point, there would be an excess supply of money and people would use the excess money to purchase bonds or increase savings causing interest rates to decrease to the equilibrium point so that borrowing would increase ● If the i was lower than the equilibrium point, there would be excess demand for money and people would decrease bonds and savings causing interest rates to increase to the equilibrium point to keep savings from decreasing too much d ● Changes in i cause movements along the M d ● Shifts in M are caused by changes in Y s s ● If the M increases in the long run, π will increase, so changes in M can only have these effect in the short run Aggregate Supply ● The most important building block of the AS curve is the Phillips Curve ● Up until 1969 there seemed to be a clear inverse relationship between inflation and unemployment ● First looked at unemployment rates and growth rate in wages ● If unemployment rates were low, demand for worker was high so wages would be higher because of competition ● If unemployment rates were high, demand for worker was low, so jobs would be held regardless of wages due to the low number of available jobs ● Changed growth rate in wages to π and this gave the Phillips curve ● Important if it is true because an economy could change unemployment rates by changing π ● Solow and Samson used this to find that if π in the US was about 4 − 5% the unemployment rate would be about 3%

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Chapter 5, Problem 24 is Solved
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Textbook: College Algebra and Trigonometry
Edition: 7
Author: Richard N. Aufmann
ISBN: 9781439048603

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Solution: In Exercises 21 to 24, find the measure of the