IMPORTANT NOTE In this study guide I have used a slightly different notation than what Dr Schlagenhauf uses in class Following the same notation in the book C is the same as Ct and C is the same as Ct 1 I did this because it is approximately fifteen thousand times easier to do in Word 1 Can you derive the household s two period budget constraint The two period budget constraint is made up of the period t constraint And the period t 1 constraint Taking these together we can derive the lifetime budget constraint equation Simply solve the t 1 constraint for St c s y t c y t 1 r s s c y t 1 r And substitute your results in for St in the t constraint equation You ll wind up with c c y t And in class he simplified it down to this y t 1 r c c 1 r y t y t 1 r That s the main equation we use for the lifetime budget constraint Remember that the left side of the equation represents the consumer s lifetime spending and the right side of the equation represents the consumer s lifetime wealth 2 Can you use the two period time model to determine current consumption future consumption and savings This is a little bit trickier than it first appears Graphing our lifetime budget constraint is as simple as drawing axes with c on the vertical axis and c on the horizontal one and then plotting a line between the intercepts find c intercept by substituting 0 for c and find c intercept by substituting 0 for c Note that you ll need to be given the other variables in this equation to do this r y y t and t and after you get that down you re going to need to find the tangency point for the utility curve and the budget constraint The tangency point is found when the slope of the budget constraint is equal to the slope of the utility curve as shown below 1 r MU c MU c 1 r MU c MU c 1 r MU c MU c 0 Where the left side of the equation is the slope of the budget constraint and the right side is the slope of the utility curve You can manipulate the equation to reach the following And then Manipulating this equation is famously counterintuitive r is given This means that you can only adjust between MUc and MUc If the left side is less than zero that means MUc is too high This means you need more current consumption It s bizarre but it s inevitable because of declining marginal utility If the marginal utility of something is too high do that thing more and the marginal utility of that thing will fall So if your marginal utility of current consumption is too high you simply need to consume more and you ll get tired of it and we can get back to equilibrium Likewise if your MUc is too high then the left side will be greater than zero so you need to increase c and you will be back to zero Once we have a tangency point at which we have established our consumption today it is a simple matter to ascertain savings borrowing Simply take current income and subtract from that current consumption like so y c s If you receive back a negative number that simply means that the consumer is a borrower 3 What is consumption smoothing Why is this important for a policy maker to understand Consumption smoothing is the tendency consumers have to want to spread out lifetime income so that it is evenly distributed The great example the Professor gave was the parking lot of a medical school where you will see students who don t earn a penny parking their Lexus that s actually the plural form of the word Lexus by the way The reason these students are going into debt like this is because their future income will be high and they would prefer to spread out their income over time Policy makers need to understand this because the policies employed to achieve numerous ends will often fall victim to the tendency of households to smooth their consumption The example we went over in class was whether or not temporary tax cuts were as effective as permanent ones for stimulating demand in a recession It s quite clear that they will not be Temporary tax cuts increase savings quite a lot as the budget constraint does not shift as far outwards and all benefits come today People will save that income for when higher taxes are reinstated 4 What does the endowment point mean Can you identify when a household is a borrower or a saver The endowment point is simply a point on the line of the budget constraint that shows what mix of current and future income the consumer enjoys An endowment point further down to the right on the budget constraint reflects a consumer who has high current income and lower future income perhaps someone who is near retirement An endowment point higher up to the left on the budget constraint reflects a consumer who has lower current income and higher future income medical students A borrower is somebody whose tangency point as described in question 2 reflects a level of current consumption that is higher than the current income shown by the endowment point A saver is somebody whose tangency point reflects a level of current consumption that is lower than the current income shown by the endowment point It makes all kinds of sense when you think about it or look at a graph but I ve noticed people make stupid errors on this all the time Make sure on the test you triple check your work on this and come back when you ve finished the test and check it one more time 5 Can you measure income and substitution effects in this framework Jesus Christ I m so tired of income and substitution effects Okay the only situation you could need to do this is when interest rate changes as this is the only thing that can cause the budget constraint to actually rotate The interest rate going up causes the c intercept to increase and the c intercept to decrease the interest rate going down causes the opposite to happen The process is the same as before Slide the second budget constraint in a parallel fashion so that it becomes tangent with the first utility function The difference between the c intercept for the fake budget constraint and the c intercept for the first budget constraint is the substitution effect The difference between the c intercept for the fake budget constraint and the c intercept for the second budget constraint is the income effect Whichever one is larger is the dominating effect 6 Can you use the framework to explain how the consumer responds to a change in some event That was pretty poorly worded but I m going to interpret it as asking …