Investment and Goods Market October 19 2016 1 31 Reminder Where is this Going We are building different markets 1 2 3 4 5 Consumers supply labor i e labor markets Consumers save to smooth i e consumption and savings Firms build capital i e investment Connect consumer savings and firm investment Short term fluctuations and monetary fiscal policy 2 31 Investment I I I I Recall the capital accounting from Production Model This is the amount spent by private businesses on capital expenditures to support future production It translates into the increase in the stock of capital K of the private sector and increases the productive capacity It includes depreciation expenditures to maintain the existing capital stock Let be the rate of depreciation It Kt 1 Kt Kt Kt 1 1 Kt 3 31 Components of Investment I Fixed Investment I Non residential fixed investment I I I Expenditures on new equipment and software Purchases of new office structures and plants Residential investment I I Construction of new homes and apartments Change in inventories usually small 4 31 Investment Share of GDP I Usually around 15 25 of GDP for most countries 5 31 Investment and the Busines Cycle I Fluctuations in investment are often the main source of short term cycles and recessions 6 31 Volatility of Investment vs GDP I I By far the most volatile component of aggregate spending 3 times as volatile as GDP 6 times that of consumption 7 31 Neo Classical model of Investment I I Related to Solow and production model of the firm but with optimal choice of capital accumulation Major modelling differences between labor and capital I I I Firm decision firms hire labor but usually own the capital Timing Labor can usually be quickly adjusted but capital takes time to install Capital lasts and it is costly to adjust and install so its future productivity matters 8 31 Firm Profits given Capital I I I I Assume again that there are only two periods Unlike the labor market section firms will own capital rather than renting it from the consumers Won t matter The cost per unit of capital is the user cost opportunity cost to the owners of the firm replacement cost etc Firm choose its desired stock to maximize profits AF K N uc K W N I Where uc is the adjusted real user cost of capital per unit of capital 9 31 User Cost of Capital In general the user cost of capital for a period of time includes two components I A depreciation component As we use the capital for production it depreciates i e I I I I Parts need to be replaced Loses economic value Needs to be upgraded to match other technological changes An interest component I I Opportunity cost to investment in capital The resources that are used for investment could have generated some interest revenue r if invested somewhere else so owners of capital have to be compensated 10 31 Desired Stock of Capital I Focus on capital so take labor as given I I Remember in labor markets we took capital as given Investment today only affects the future capital stock K f 1 K I I I Choosing I amounts to choosing K f so directly choose K f Assume that firms are able to finance any investment from public financial markets without any frictions so in the present they can set K f and only need to worry about paying the costs for the capital tomorrow 11 31 Desired Capital Stock I To choose K f today needs to know I I I the user cost of capital tomorrow the return of a marginal unit of capital tomorrow The firm chooses its desired K f to maximize profits n o max Af F K f N f ucf K f wf N f Kf I FOCs with respect to K f Af F K f N f K f z ucf z 0 marginal cost Future marginal product M P Kf M Cf 0 I Remember we are leaving N and N f completely flexible I I Could combine with decisions in the labor markets model We normalized so that all tax terms are all in the user cost 12 31 Optimal Level of Capital I The desired K f is reached when the slope of the production function equals that of the cost I I I If M P K M C gains to increase K further If M P K M C then capital expensive so reduce If M P K M C optimum no improvements possible 13 31 Optimal Investment and the User Cost of Capital I Depreciation rate is known so once the firm computes the desired K f if capital can be freely adjusted right away optimal investment today is I K f 1 K I Two alternative choices for investment capital unit 1 Can get M P K f tomorrow and then resell the capital left tomorrow 1 2 Sell the unit of capital today at and earn interest to obtain 1 r tomorrow I In equilibrium the two investment possibilities have to yield the same return no arbitrage M P K f 1 1 r 14 31 User Cost in Equilibrium I Rearrange the user cost formula M P K f 1 r 1 I Recall the firm s optimal choice is such that ucf M P K f I Then ucf r I So in equilibrium unit user cost is the foregone interest rate depreciation rate 15 31 User Cost Equlibrium I I Checking for optimality from the book Why is M P K f decreasing in K 16 31 Comparative Statics of MPK For example a change in future productivity I Each unit of capital is more productive so invest more The optimal amount of K f goes up 17 31 Change in Future Productivity I Alternatively looking at directly with M P K f and uc 18 31 Comparative Statics of User Cost I Changes in r show up in the user cost ucf r I Increase in r I I It becomes more profitable to put profits in a bank so the opportunity cost of holding capital increases ucf Increase in I Capital depreciates more so it becomes more costly to hold capital ucf 19 31 General Effect of User Cost I If the user cost increases from uc1 to uc2 the cost curve shifts up I Each unit of capital is more costly so invest less The optimal amount of K f goes down 20 31 Example Change in Interest rate 21 31 Other Determinants of Desired Capital Stock I Current productivity goes up I I No effect on K f only future productivity matters Future labor goes up I If production function is Cobb Douglas then production curve moves up each unit of capital is more productive so K f goes up 22 31 Short Run vs Long Run Two basic stages 1 Short Run factors that can adjust immediately and without cost or other frictions adjust immediately I example labor supply labor demand 2 Long Run factors that required time to adjust …