a) The marginal tax shows how large fraction of an increase in income that is
paid in tax. We get it by taking the derivative of the tax function with respect
dT (Y )
If Y = 0 we get T =T (Y ) =0,5 0 20 =20 so this is the interce
1. Endogenous variables are explained within the model while exogenous variables
are taken as given. This means that we can use the model to understand how a
change in one exogenous variable affects the endogenous variables in the model if
a) If Karl abstains from 52 hamburgers this year he can eat 53 hamburgers next
52 4 (1 + 0.045)
b) One plus the real interest rate is how many hamburgers you get next year if
you give up one hamburger today:
1.02; r 0.02.
a) a) au = 1 + au n + z
( 1 + z ) + u n
L = + ( 1 + z ) + u n
c) We take the first order condition with respect to :
2 2 ( 1 + z ) + u n =
a 2 ( 1 + z ) au n =
+ z + au n )
d) Higher inflation in the past mea
a) We can write Yi = Pi P Y and take the derivative:
= Pi 1P Y ,
P P Y
Pi 1P Y i =
b) The inverse demand function shows what price you have to set to sell a certain
quantity. Solving the demand function for the
C 0 is the intercept of the consumption function, how much consumption will
be at zero income. We can think that, at zero income, the typical consumer
would consume out of his assets.
The slope b is the marginal propensity to consume wh
a) Assuming that the other 50 percent is put in financial assets we get:
Liabilities and owners equity
a) The government uses goods and services which are produced by the private
sector. Therefore, the government share of use (consumption and investment)
is larger than the share of production.
b) A substantial share of government income (mainly tax reve
1. Since core inflation is on target the deviation from target of CPI inflation may be
due to rising energy prices or changes in indirect taxes, for example. If these
effects are perceived as temporary, the central bank can let them pass without
= qY = = 1
x Y *
x ( ) Y
Y = a + bY bT + c di + G + x qY
c) Y bY + qY = a bT + c di + G + x
a bT + c di + G + x Y *
1 b + q
1 b + q
A high marginal propensity to consume (b) increases t
1. They are both forms of fixed exchange rate regimes in the sense that the Central
bank has a target level for the exchange rate and tries to keep the exchange rate
close to that target, and that this is the main objective of monetary policy. In the
a) A permanent improvement in technology raises trend production and the
natural level of production. What happens to the cyclical part (the trend
deviation) depends on monetary policy but if the central bank keeps
production at the natural level the c
a) The employment rates are 74 percent for men and 64 percent for women.
b) The unemployment rates are 7.5 percent for men and 8.6 percent for women.
a) Job finding rates:
b) The duration of unem
a) If K=10 and N=40 production is Y =
10 40 = 20.
b) If K=20 and N=80 production is Y =
20 80 = 40.
c) With this production function there is constant returns to scale so a doubling
of inputs leads to a doubling of production.
a) The capital stock i
1. We have =
so using the rule of thumb for percentage changes:
+ * .
According to the interest parity condition
i * and thus
= i* i + * .
Substituting the numbers we get 0.02=0.04-i+0.03-0.02. Thus i=0.03: the interest
rate must be t
a) In this case, the marginal utility is
for consumption is
d ln ( Ct ) 1
so the first order condition
1 / C1
= 1+ r .
(1 / C2 ) / (1 + )
b) Solving the first order condition for C2 we get
Substituting into the lifetime budget
1. One should never quarrel about definitions. Anybody has the right to define
money as he or she wants. The question here is whether these assets have the
four characteristics that money has in our model.
Gold was used as means of payment long ago but it