Business InvestmentSlide 2Slide 3Gross & Net InvestmentThe Optimal Level of CapitalSlide 6Slide 7PowerPoint PresentationSlide 9Accelerator Model Implications for the Business CycleSlide 11Slide 12Slide 13Slide 14Slide 15The “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 Demand Growth Rates in Sales and Served MarketsHistorical Patterns in Aerial Work Platform Demand Cyclical 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 categoriesThe 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 growth so much greater than those in output growth?”BRINNER410.pptGross & Net InvestmentI is “gross investment”I-CCA is “net investment”a capital stock rises from period to period by the amount of net investmentor I(gross)=I(replacement)+I(net)K (Capital this period)== K\1 + I (gross) - D = K\1 + I (net)BRINNER510.pptThe Optimal Level of CapitalSimple 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 CapitalK / Y = ($2500+$2500) / $5000 = 1Thus Optimal=Necessary K = 1 x YIf Y is constant at $5000, then so must be KK 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 CapitalWhat if the producer wants to boost output (Y) by 3% to $5150?K must rise to $5150, meaning I (net) must be $150added to I(replacement) $350implies I(gross) = $500So investment in that year is 10% of outputIn fact, these are the numbers for the USMachines & Factories Required to Produce Output020004000600080001000012000195919611963196519671969197119731975197719791981198319851987198919911993199519971999$ 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 CycleNote how variations in Y get amplified in variations in IA $150 change in Y required a $150 change in IOr, a 3% change in Y required a 40+% change in IRealistically, 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 CapitalI = 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 CapitalIn 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 fixedThe 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 CapitalY= 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 Capitalmarginal product of capital = b * average product of capitalBRINNER1410.pptThe Optimal Level of CapitaldY/dK=marginal product of capital= b * Y/K = b * Avg. Product of CapitalThe real price paid per unit of capital is Pk / PyIn equilibrium, this price is its marginal product•Thus Pk/Py = b * Y /KSolve 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 CapitalThe price paid per unit of capital is Pk / PyIn equilibrium, this price is its marginal productPk/Py = b * Y /KWhat 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 CapitalThe 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 PointsIn 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 expectationsBRINNER1810.pptExamples from a specific companyThe company manufactures equipment used to facilitate construction:»Aerial work platforms (“AWP” in next slides for lifting people ; 2 types--”scissor
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