Business InvestmentBusiness InvestmentBusiness InvestmentGross & Net InvestmentThe Optimal Level of CapitalThe Optimal Level of CapitalThe Optimal Level of CapitalAccelerator Model Implications for the Business CycleThe Optimal Level of CapitalThe Optimal Level of CapitalThe Optimal Level of CapitalThe Optimal Level of CapitalThe Optimal Level of CapitalThe “Price or Cost” of CapitalTransitions between Targeted Equilibrium PointsExamples from a specific companyHistorical Patterns in Aerial Work Platform Demand Growth and Volatility of Industry SalesHistorical Patterns in Aerial Work Platform DemandGrowth Rates in Sales and Served MarketsHistorical Patterns in Aerial Work Platform DemandCyclical Forces Driving Sales around the Rising Penetration TrendHistorical Patterns in Aerial Work Platform DemandHistorical Patterns in Aerial Work Platform Demand Cyclical Forces Driving Sales around the Rising Penetration TrendBRINNER110.pptBusiness InvestmentLecture 10BRINNER210.pptBusiness Investment “Investment”: not “financial” in the everyday sense but purchases of plant & equipment, (or additions to inventories) “I” is demand today, supply tomorrow; unique among GNP spending categories The capacity created by I is flexible (through variation in shifts, maintenance schedules, etc) so purchase can be delayed in tough timesBRINNER310.pptBusiness Investment-10%-5%0%5%10%15%20%198319851987198919911993199519971999Investment Growth Real GDP GrowthA key question for economists seeking to understand the business cycle was: “Why are the cycles in investment growthso much greater than those in output growth?”BRINNER410.pptGross & Net Investment I is “gross investment” I-CCA is “net investment” a capital stock rises from period to period by the amount of net investment or I(gross)=I(replacement)+I(net) K (Capital this period)== K\1 + I (gross) - D = K\1 + I (net)BRINNER510.pptThe Optimal Level of Capital Simple World: It takes· one $2500 machine· housed in a $2500 building· plus $3000 of labor · to make $5000 of output.· Machines last 10 years, buildings 25, decaying linearly.· No substitution is possible.BRINNER610.pptThe Optimal Level of Capital K / Y = ($2500+$2500) / $5000 = 1 Thus Optimal=Necessary K = 1 x Y If Y is constant at $5000, then so must be K K decays/depreciates each year by · 10% x $2500 (equip)=$250· 4% x $2500 (building)=$100· thus I (replacement) must be $350 per year to keep K stable at $5000, with $2500 of each type of KBRINNER710.pptThe Optimal Level of Capital What if the producer wants to boost output (Y) by 3% to $5150? K must rise to $5150, meaning I (net) must be $150 added to I(replacement) $350 implies I(gross) = $500 So investment in that year is 10% of output In fact, these are the numbers for the USMachines & Factories Required to Produce Output020004000600080001000012000195919611963196519671969197119731975197719791981198319851987198919911993199519971999$ BillionReal GDP Private CapAccelerator Data: Change in Output vs Levels of Gross & Net Investment$(200)$-$200$400$600$800$1,000$1,200$1,400$1,600195919611963196519671969197119731975197719791981198319851987198919911993199519971999Change in Real GDP Gross Investment Net InvestmentRecent shift to even higher investment relative to GDP is due to new technology opportunitiesNote: Net Investmentroughly matches theUS change in GDPBRINNER1010.pptAccelerator Model Implications for the Business Cycle Note how variations in Y get amplified in variations in I A $150 change in Y required a $150 change in I Or, a 3% change in Y required a 40+% change in I Realistically, the response to an output change isn’t so sudden, and the base level of investment includes some net addition because output is trending upBRINNER1110.pptThe Optimal Level of Capital I = I(gross)= I (replacement) + I(net)• I (replacement)=dep. rate x K = c1 x K=c1 x Y• I (net) = c2 * [ Y - Y \1] I = c1 * Y + c2 * [ Y - Y\1 ] Note that the level of investment is a function of the change (the first derivative) in output; By extension, the growth of investment (the first derivative) is a function of the acceleration (the second derivative) in output: Hence the Accelerator Model of InvestmentBRINNER1210.pptThe Optimal Level of Capital In a more realistic model, production can temporarily rise without adding K by adding a shift or overtime or delaying maintenance, thus c1 is not rigidly fixed, and new capital- or labor saving technology can be introduced so c2 is also not rigidly fixed The microeconomic basis of c2: the optimal capital-output ratio• relative prices and productivity for capital , output, and labor determine this• the first basic extension is the Cobb-Douglas production modelBRINNER1310.pptThe Optimal Level of Capital Y= KbL(1-b) dY/dK=marginal product of capital = bK(b-1)L(1-b)» =b (1/K) KbL(b-1)» =b (1/K) Y» =b Y/K = b * Average Product of Capital marginal product of capital = b * average product of capitalBRINNER1410.pptThe Optimal Level of Capital dY/dK=marginal product of capital = b * Y/K = b * Avg. Product of Capital The real price paid per unit of capital is Pk / Py In equilibrium, this price is its marginal product• Thus Pk/Py = b * Y /K Solve for K to find the optimal K:• K = b * Py/Pk * Y Or the optimal K/Y ratio = b* Py/Pk• Just like the simple fixed coefficient model, except the ratio is now sensitive to the real price of capitalBRINNER1510.pptThe Optimal Level of Capital The price paid per unit of capital is Pk / Py In equilibrium, this price is its marginal product Pk/Py = b * Y /K What is b, that is how can it be interpreted beyond “the exponent of capital”?• b= (Pk * K) / (Py * Y)• = capital income / total income• hence the capital share of incomeBRINNER1610.pptThe “Price or Cost” of Capital The cost of funds (“r”)... ...minus price appreciation of the real asset (“inflation”)... ...plus the cost of perfect maintenance = the rate of depreciation (“d”) So the cost, Pk/Py = r - inflation + dBRINNER1710.pptTransitions between Targeted Equilibrium Points In practice, future K (K*) is targeted to hit the optimal level consistent with an expected future path of Y (Y*) given an expected cost of capital ( (Pk/Py)* ) K* = b Q* (Py/Pk)* Economists add lag structures to reflect
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