ECON 352x 1st EditionExam # 2 Study GuideInvestment plays a crucial role in economic growth and fluctuates sharply over the business cycleAssumptions:1. Assume the typical firm that produces the economy’s output is competitive. It takes price of its output (P) and price of inputs --wage rate (W) and rental rate of capital (R)-- as given. Firm’s actions do not affect prices.2. Firms maximize profits (= revenue – costs): P = PY – WL – RK = P F(K,L) – WL – RKLaborChange in Profit = Change in Revenue – Change in Cost = (P x MPL) – W– If MPL > W/P, firm can  profits by  L---If MPL < W/P, firm can  profits by  LHire labor up to where MPL= W/Pw = W/P is the real wage; in units of outputThe MPL schedule is the firm’s labor demand curve and when MPL is decreasing, the labor demand curveis downward sloping CapitalChange in Profit = Change in Revenue – Change in Cost = (P x MPK) – RIf MPK > R/P, firm can  profits by  KIf MPK < R/P, firm can  profits by  KInvest capital up to where MPK= R/PR/P is the real rental price of capital (also called the user cost of capital, uc), and is equal to the (real) interest rate (r) plus the depreciation rate (d): uc = r + dThe MPK schedule is the firm’s capital demand curve and when MPK is decreasing in K, the capital demand curve is downward slopingThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Cost of CapitalRent its entire capital stock from a rental firm, which just invests in new capital and rents out the capital; firms usually do both Separate cost of renting “K” and cost of buying “I” Firm’s cost of capital for a unit: CoC = i PK - DPK + d PKPk: Purchase price of new investment good; i: nominal interest rate; change in Pk: capital gain; d: rate of depreciationCoC = PK (i - DPK/PK + d)It is typical to assume that (DPK/PK) grows at the rate of inflation, and r = i – inflation- or real interest rate is equal to nominal interest rate minus inflationThus we can write unit nominal cost as: PK (r + d)Marginal user cost (in real terms): uc = PK (r + d) / P We assume that price of capital PK is equal to P (Note that the book defines PK as the real price ofcapital, and uc as the dollar user cost of capital). Therefore uc = r + dMarginal revenue: MPKIf firms are maximizing profits, we therefore get the condition:MPK = r + dThis equation determines the desired capital stock that firms have to invest, denoted Kd“r” enters cost of investment in new capital, thus the desired capital stock depends on r, denoted Kd(r)Taxes and Cost of CapitalIf f is the marginal tax rate for firms profits, then MPK (1-f ) = R/P = r + dThis gives: ffdrPRMPK111this is the cost of investment in new capitalTaxes reduce after-tax revenuesThis requires a higher MPK to pay the same uc=r+d Taxes combined with the current treatment of inflation affect greatly the after-tax returns for consumersTaxes are levied on consumers nominal savings. The income tax rate is denoted c After-tax nominal returns is: iAT = iBT (1-c)InvestmentThe implied real returns are: rBT = iBT -  rAT = iAT - = iBT(1-c) -  (where  is inflation)How is investment determined in equilibrium?1. MPK determines the amount of desired capital: Kd(r)2. Firms have to invest Id to achieve their desired capital stockLet K0 be the current (or initial) capital stock. Capital depreciates at rate d, so d*K0 has to be replaced The desired investment is then determined byKd = K0 – d*K0 + IdThus the desired investment is: Id = Kd – (1 – d) K0Definitions:Id = Kd – (1–d) K0 is called Gross Investment(Kd – K0) is called Net InvestmentProperties of investment:Kd(r) depends on r, thus Id depends on r. We write: Id(r)Kd(r) is decreasing in r, thus Id(r) is decreasing in rCombine all the firms’ demands for investments to get the aggregate demand for investmentId(r) is decreasing in r, hence the demand for investment is a downward sloping curveGood Market EquilibriumIn the goods market equilibrium, the total demand for investment must be equal to the economy-wide savingIn a closed economy: Id(r) = Sd(r)(desired savings = desired investment)The goods market equilibrium yields an optimal level of investment I* and and equilibrium interest rate r*Terms to know: KdDesired capital stockIdImplied desired investment flowi The nominal (market) interest rater The real interest rated Rate of capital depreciationR/P Real rental rate of capitalPkPurchase price of new investment goodsDPkCapital gainsf ,cTax rates on firms and consumers, respectivelyiBT, rBT Before-tax nominal and real interest rate, respectivelyiAT, rAT After-tax nominal and real interest rate, respectively Inflation rateCh. 6 Growth= rise in real GDP per capitaCan we grow forever? Can we grow richer forever? Where does growth come from?Solow model tells about GDP over time; productive function tells about the GDP todayGrowth accounting can help us decompose growth and inform us about the sources of growthWe can relate the growth rate of output to the growth rates of inputs by the following equation:change in Y/Y = change in A/A + aK (change in K/K) + aL (change in L/L)change in A/A is the growth rate of total factor productivity; the rest of the equation is the total input growth aK is the elasticity of output with respect to capital aL is the elasticity of output with respect to laborIf you know the growth rates: DY/Y, DK/K, and DL/L, you can “back out”:The growth rate of TFP: DA/A (A’s are called Solow residuals)The growth rate of labor productivity: DAL/ALwhen you rearrange the equation: change in (Y/L) / (Y/L) = change in A/A + aK change in (K/L) / (K/L)growth rate of GDP per worker= growth rate of TFP plus growth rate of capital labor ratioY/L is GDP per employed person; K/L is the capital labor ratioGrowth in Labor, L, comes from:–population growth (from all sources)–increases in labor participationGrowth in Capital, K, come from:–Net investment (enabled through saving)Growth in TFP, A, comes from:–Innovation–A large list of forces (institutions, markets, culture,…)Least understood and yet the most important elementThe 1970’s saw a sharp decrease in TFP due to measuring quality improvements is hard, health, environment, and worker safety regulations, and large increase in oil prices. Also,