ECO 5 GREATEST HITS (1st PART)

Measuring the economy

• Three approaches to measure GDP
  

  product , income, and expenditure approach
  why do the three approaches (should) deliver the same result?
  Income-Expenditure identity:
  

  Y=C+I+G+NX
  
  

• stocks (wealth, capital,..) and flows (income, investment, saving)
• Savings, the Current Account, and the Balance of Payments
  

  Uses of savings identity: S=I+CA
  where CA=NX+NFP
  what do savings have to do with net exports?
  

  Capital Account= increase in foreign-owned assets in Mexico - increase in Mexican owned assets abroad (private and official) = -CA
  

  this is why financial crises are often preceded by large CA deficits: the country had been accumulating debt (importing more than exporting) which -for different reasons- was not able to repay. And also why they are followed by CA surpluses: the country is paying back all- or part of- the debt.
  

  private and government savings:
  S_p=I-S_g+CA (twin deficits)
  

  Low savings in Latin America (and therefore, either Current Account deficits or low Investment) are generally not caused by Government dissavings (S_g<0), but by very low private savings
  

  therefore we need a model that explains private consumption (and implicitly private savings as well) $\rightarrow$ Permanent Income Model

• Price Indices: CPI, GDP Deflator
  

  If utility function is Cobb-Douglas:
  

  $$U(X,Y)=q*X^\gamma Y^{1-\gamma}$$
  
  
  
  
  $$CPI=P_X^\gamma P_Y^{1-\gamma}$$
  
  
  and "real" income (in terms of utility levels achievable with that amount of income) is $\frac{Z}{CPI}$
  

  in terms of units of the tradable good X:
  

  $$\frac{\hat{Z}}{p^{1-\gamma}}$$
  
  
  where $p=\frac{P_Y}{P_X}$ and $\hat{Z}=\frac{Z}{P_X}$
  

  as long as the relative prices of non tradable goods are different across countries, the standards of living (real income) corresponding to a given amount of money (US$, Pesos) are different.
  

  This is why Mexican GDP is roughly a fifth of US GDP when measured in $, and only a third when measured in "real" terms, that is, in terms of utility levels.

Intertemporal choice in an endowment economy

• to keep things simple, we start by abstracting from issues of production: take output as given, and focus on the consumption choice
  

• The intertemporal problem: trade-off between consuming today and consuming tomorrow
  

  the impact of interest rate increases on savings: substitution and income effect.

  the intertemporal trade-off:
  Marginal Rate of Substitution (MRS) = Marginal Rate of Transformation (MRT)
  

  $$\frac{U_1(C1,C2)}{U_2(C1,C2)}=(1+r)$$
  
  

• Permanent Income
  

  Since individuals enjoy to consume roughly an equal amount in both periods, if can borrow and lend they will try to smooth consumption over time: their consumption will not depend on the time pattern of income, but only on its present value, that is, the permanent income
  

  if utility is logarithmic and $\beta(1+r)=1$:
  

  $$C1=C2=\frac{1+r}{2+r}(Y1+\frac{Y2}{1+r})$$
  
  
  the Permanent Income theory implies that consumption fluctuates less than output, which is roughly what we observe in the data

• the interest rate in a closed economy
  

  in a closed -endowment- economy people are bound to consume their income, so what the theory delivers is a prediction for the equilibrium real interest rate
  

  
  

  $$(1+r)=\frac{Y2}{Y1\beta}$$
  
  
  the real interest rate is countercyclical in a closed economy (move in the opposite direction of the business cycle)

• Ricardian Equivalence:

  the timing of taxes is irrelevant, for a given time pattern of government spending
  

  where do we get Ricardian Equivalence from?
  Permanent Income:
  

  $$C1=C2=\frac{1+r}{2+r}(Y1-T1+\frac{Y2-T2}{1+r})$$
  
  

  + Intertemporal Budget Constraint of the Government:
  

  $$G1+\frac{G2}{1+r}=T1+\frac{T2}{1+r}$$
  
  
  therefore
  
  $$C1=C2=\frac{1+r}{2+r}(Y1-G1+\frac{Y2-G2}{1+r})$$
  
  

  Holds also in a closed economy

  important policy implication: reducing current taxes is no way of stimulating consumption, because consumers understand this and will save more in order to be able to pay for higher future taxes
  

  borrowing constraints

• the Current Account in an endowment economy
  
  
  $$CA=S_p+S_g=Y1-C1-G1=Y1-\bar{Y} - (G1-\bar{G})$$
  
  
  where $\bar{Y}$ and $\bar{G}$ are respectively permanent income and permanent government spending
  

  countries that are growing tend to run CA deficits - other things being equal

  countries that have high temporary government spending (wars) tend to run CA deficits - other things being equal
  

  second important implication from Ricardian equivalence: raising current taxes has no impact whatsoever on the CA. even if S_g increases, S_p will decrease (people know that they will pay less taxes tomorrow) and the CA will not be affected
  

  welfare gains from capital mobility in an endowment economy

the production function

• decreasing returns to scale in both capital and labor
  F_K(K,N)>0 and decreasing in K
  F_N(K,N)>0 and decreasing in N
  
• homogeneity of degree one, product exhaustion
• constant factor shares
• Cobb Douglas: $F(K,N)=AK^\alpha N^{1-\alpha}$

Intertemporal choice in a production economy

• The intertemporal trade-off with production:
  MRS = MRT
  
  $$\frac{U_1(C1,C2)}{U_2(C1,C2)}=F_K(K,N)+ (1-\delta)$$
  
  

• capital accumulation in a closed economy:
  
  $$K2=\frac{\alpha\beta}{1+\alpha\beta}Y1$$
  
  
  the role of :
  
  • preferences($\beta$)
  • productivity($\alpha$)
  • available resources (Y1)
• the decentralized equilibrium:
  investment and savings as a function of the interest rate
  

• notice that consumption is only a fraction of Y1: if Y1 increases (decreases) by 1 Peso, consumption will increase (decrease) by less than that $\rightarrow$ Permanent Income

• the interest rate in a closed economy with production
  
  $$r \simeq \ln(A)+(\alpha-1)\ln(Y1-G1)+\ln(\alpha) +(\alpha-1)\ln(\frac{\alpha\beta}{1+\alpha\beta})$$
  
  

Investment and capital mobility in the open economy

• In an open economy investment is determined by:
  
  $$(1+r^w)=F_K(K,N)+ (1-\delta)$$
  
  

• with exogenous labor supply, domestic preferences do not affect investment
• implications of capital mobility for developing countries:
  countries with low per capita capital have higher MPK -other things being equal- (which implies a higher return to capital) and therefore represent an attractive place to invest in
• welfare gains from capital mobility in an endowment economy
• the current account in a production economy

Labor demand, Labor Supply, and Structural Unemployment

• Labor demand:
  
  w=F_N(K,N)
  
  

• cross country differences in real wages due to differences in the per capita capital (human and physical)
• Labor Supply:
  
  U_c(C,L)w=U_L(C,L)
  
  
  trade off between consumption and leisure
• Equilibrium in the labor market
• Definitions of Unemployment
• Okun's Law
• Explanations for Structural Unemployment (the Natural Rate)