Question: 4 country a is located on a small island that...
4. Country A is located on a small island that is isolated from the outside world. The country has one representative consumer, whose preference is represented by:
U(c,l) = ln(c) + ln(l)
There is one representative ﬁrm in the economy which is owned by the consumer, it produces one type of good that can be used for consumption or government expenditure using capital and labour as inputs. The ﬁrm owns the capital it uses and it’s production technology is represented by
F(K,N) = zKαN1−α
where z is the total factor productivity, and α is the capital share of income. The ﬁrm pays all of its proﬁt back to consumer as dividend. The government of country A spend a pre-determined G amount of goods to provide public services, and it taxes consumer through a lump-sum tax t to ﬁnance the expenditure. the government’s budget is balanced:
G = t
Now, suppose that the ﬁrm cannot change its capital stock, or improve its production technology in the short period, such that z and K are given.
(a) When describing this economy as an macroeconomic model, what is the set of exogenous variables? What is the set of endogenous variables that can be determined given the set of exogenous variables using the concept of Competitive Equilibrium?
(b) Deﬁne the competitive equilibrium for this economy, be speciﬁc about what it is, what conditions have to be satisﬁed, who solves what problem and etc.
(c) List the set of equations that will be used to determine all of the endogenous variables. Which four of these endogenous variables are essentials, such that once you know these four, all other endogenous variables can be obtained easily?