Midterm Macro

Question 1

Formula de sumatoria geométrica infinita

Answer 1

Σt:0->∞ = a(b)^t= a(1/1-b)
(Así eliminamos “t”)
Normalmente:
Σ t:o->∞ = Ct /(1+r)^t

Question 2

Competitive equilibrium

Answer 2

A set of allocations {c, l, n^s, n^d, y, g} where: (1) solves utility and profit π, maxilization problem, (2) markets clear: c + g= y, and n^d=n^s (3) government b.c. is ballanced: g=twns

Question 3

Competitive equilibrium elements

Answer 3

c: consumption, l: leisure, ns: labor supply, nd labor demand, y:output, g: government revenue(tax).

Question 4

Gov revenue formula

Answer 4

T(w*ns)

Question 5

Total wage income

Answer 5

W=w*n^s

Question 6

Maximization problem of Representative Firm

Answer 6

Ej.
U(c, l)= c+(2-l)l
Technology (z): y= 2nd
Max n^d, π: y-wn^d,
s.t. y=nd

Question 7

Government Budget Constraint

Answer 7

G = T
Income expenditure identity:
y= c+ g
What’s c?
C= Wn^s + π - T
C= wn^s + y-wn^d - G
Technology
Y = z*F(k,n) ->y=zF(K, H-l)

Question 8

Euler equation

Answer 8

Intertemporal optimality condition that relates MUc in two or more periods.
It s often a consumption choice about whether to consume or save (or other affairs). Represents the equality of MU of consumption in both periods, adjusted for the interest rate + future expectations
It relates MUc in the two periods.
ej:
(1) U’ = λ1
(2) βU’ =λ2
Normalmente reemplazas λ1 con el resultado de la FOC (3) y resultsdo incluye (1+r)

Question 9

Firm maximization problem

Answer 9

Max(y, n^d)
π = y -w*n^d

Question 10

Pareto efficient allocations?
FWT conditions

Answer 10

P. A. Need to (1) be Feasible, (2) and there are no other feasible allocations.

FWT states that a Competitive Equilibrium is pareto efficient. if (4):
1. No externalities
2. Perfect Competition
3. Full information
4. No transaction costs,