Ch 4 Investment Tuesday October 15 2013 9 13 PM 1 2 Y C I G X For Long Run Growth a Division of resources between C and I is crucial 3 SR i Investment 4 a b Consumption is huge of GDP Most fluctuation in GDP are from investment Investments are very volatile from year to year a Business spending in capital i Leads to increase in K capital stock b Recall that I Kf 1 d Kt 5 Fixed Investment a b Non residential PPE 6 Residential Investment a Construction of homes and apartment 7 Labor hiring decision vs Capital hiring decision Difference between labor and capital Own vs Rent Hire workers but own capital a b c i Timing i ii Hire fire can be done quickly Have to be forward looking with capital d Capital lasts costly to adjust i ii Future productivity matters Capital stays with firm longer 8 Neoclassical Model of Investment a 2 periods to take in to consideration when decision is made i Current and future b c Based on what you expect for the future Pk PFk i ii Price current capital Price future of capital d The Model i Assumptions 1 2 Take N as given constant Firm chooses desired stock of future capital to maximize profits ii Why focus on future capital and not investment 1 Kf 1 d K I a b c I Kf 1 d K K was determined in the past K and d are given iii Maximization iv Derivation of profit max of Kf 1 2 User Cost of Capital e Leads to that Future MPK user cost Future Marginal benefit marginal cost i Suppose firm has capital they can 1 Hold onto capital use next period a b Produce MPK f Sell capital left over for 1 d Pk f 2 Sell capital and earn interest a b Pk price now Interest in future 1 r Pk In equilibrium should get same return from 1 or 2 ii 1 1 a b Marginal benefit marginal cost User cost of capital i ii Net cost of capital Price you bought it at Pk interest rate you gave up rPk money received next period 1 d pk f Int Macro lecture notes Page 1 money received next period 1 d pk f 2 If Pk Pk f a Uc mpk b f Comparative Statics i Suppose Af up then Kf will be more productive 1 2 3 Future Tech Progress Means that MPKf will be up Kf up means more investment now ii Change in uc component r d Pk or Pk f UC 1 r Pk 1 d Pk f 1 2 iii Increase in 1 Real interest rate a Capital more expense Kf down I down 2 Depreciation Rate 3 Price of K current a Less left over Cost of capital more expensive Kf down a More expensive to hold capital now less K now less Kf 4 Future price of capital a b c Receive less when you sell capital in future Increases net cost of holding capital Less K now and in future 5 N f or A f a Future MPK increases More Capital 9 Why is investment so volatile a b K stock is than investment Levels i ii K big I small c Therefore I must change by a lot to affect K even a little Int Macro lecture notes Page 2 Ch 4 Consumption Friday October 18 2013 2 17 PM 1 2 How much to consume and how much to save Simple model of Consumption a b c d e Current consumption Future consumption cf Constrained by income and wealth a assets at beginning of current period af beginning of future Intertemporal Budget Constraint 3 a Budget constraint today Y a c af i b Future Budget constraint i cf Yf af 1 r 1 Total income and assets what I consume now and future assets 1 2 3 Earn income in future earn interest on assets in first period All equals consumption since I consume all at end of period c Combine for Intertemporal Budget Constraint i cf Yf 1 r Y a c 4 Lifetime Intertemporal Budget Constraint Rearrange intertemporal bc a i 1 Left side a 2 Right Side Present value of lifetime consumption a Present value of lifetime resources PVLR 5 Lifetime Utility Function a U c cf 1 u c u cf i Left side 1 ii u c and u cf Total lifetime utility 1 2 Utility from consumption today and in the future Beta is discount rate to make it relative to today b Properties of u c and u cf i u x 1 Increasing concave function 6 Utility maximization a i Subject to b Plug in Int Macro lecture notes Page 3 i i i 1 1 1 2 3 c d FOC and rearrange to obtain Consumption Euler Equation Optimal Consumption Equation 1 If one additional real dollar today Consume today and receive u c Save 1 r real dollars utility u and discount it by B a b If a If a 2 3 Consume more today Consume more in the future 7 Optimal Savings for log utility a Solve FOC i Cf B 1 r c b Plug into the budget constraint of w ii Get final answer 8 Comparative Statics a Price of consumption i ii iii Opportunity cost of consuming today Price of c 1 r cf Price of cf 1 1 r c b Private Government and National Saving i Private saving current disposable income current consumption 1 Spvt Y T C ii National saving 1 Spvt T G iii Future consumption does not matter for current saving c Increase in Real Interest Rate i ii Relative price of c has increased Substitution Effect As r increases more expensive to consume today consume more in the future iii Income Effect More interest for same saving C up cf up Spvt down As r increases PVLR increases Save a b Borrow a b Worse off Need more to pay off later C down cf down Spvt up d Y increase i ii PVLR increases C and cf increase Int Macro lecture notes Page 4 i When consumption and saving is relatively equal Not too much in one period b Recall optimal consumption condition ii iii iv C and cf increase Pure income effect Spvt Y C 1 Yf increase e Since both Y and C big Savings greater also i ii iii iv v PVLR increases C and cf increase Pure income effect Y is unchanged but c has increased Spvt decrease Consumption Smoothing When c cf a 9 i ii iii u c u cf Utility maximizing bundle is at c cf Consumption smoothing does NOT hold 10 Deviations from consumption smoothing a Recall optimal condition c d e Plug in c cf B 1 r 1 If B 1 r 1 i i b Time preference B Assume r 0 If 1 i a B 1 u c u cf i Consumption smoothing makes sense Consumption is same whenever B 1 B 1 r 1 u c u cf c …