ECON 2500 Lecture Notes - Lecture 27: Royal Society Of Literature, Budget Constraint, Real Interest Rate

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Econ 2500 lecture 27 notes the representative consumer. The representative consumer is a price-taker who takes w, woe, and r as given. Taxes are also given from the consumer"s point of view. Disposable income in the current period is then split between consumption and savings, and savings takes the form of bonds that earn the one-period real interest rate r. Just as, savings can be negative, in which case the consumer borrows by issuing bonds. The consumer"s current budget constraint is then c + sp = w(h - l) + p - t. (11-1) Just as we can substitute for savings sp in equation (11-1) using equation (11-2) to obtain a lifetime budget constraint for the representative consumer: c + coe 1 + r = w(h. L) + p - t + woe(h - loe) + p oe - toe 1 + r . (11-3)

Related Questions

Consider the one period model with endogenous labor supply we studied in class, where workers (consumers) are born with one unit of labor effort and no physical endowments. The total population of consumers is one. Furthermore, assume that workers have the following lifetime utility function: U(c, l) = ln c + ln l Production takes place by a representative firm that has access to a production technology of the Cobb-Douglas form: Y = AK Î± L 1âÎ± and as usual profits are rebated back to consumers and P = 1. Unlike the model discussed in class, the firm pays (w + Ï ) for every unit of labor time used, Ï > 0 is a unit tax imposed by the government (or some type of regulation). In this manner, the firm pays ÏL to the government and wL to workers. Finally, the government does no collect taxes from workers but only from employers as mentioned above. Government revenue is used to finance spending, G where G does not directly affect the economy. The governmentâs budget constraint is such that: ÏL = G

A. Write down the individualâs problem of utility maximization. Be sure to derive the budget constraint for the problem. Provide economic interpretation for this model.

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 fi rm 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 fi rm owns the capital it uses and it's production technology is
represented by
F(K;N) = zK^aN^1-a
where z is the total factor productivity, and a is the capital share of income. The fi rm pays
all of its profit back to consumer as dividend.
The government of country A spend a predetermined 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) Defi ne 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?
(d) Write down the four equations that can be used to solve for these four essential endogenous variables, and describe where do they come from. Describe in details the steps of
how would you solve for the competitive equilibrium (without actually solving for it ).
(e) Setup the Social planner's problem for this economy. What is the marginal condition
that pins down the planner's choices.
(f) Now, describe what would happen to c, l, and w if the firm had more capital, such
that Knew > Kold.

ECON 2500 Lecture Notes - Lecture 27: Royal Society Of Literature, Budget Constraint, Real Interest Rate

ECON 2500 Full Course Notes

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