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ECON206
PROBLEM SET 2
1. Consider a closed economy described by the following equations
Y=15000
G= 3000
T= 3000
I= 4000-50r
C=100+ 0.70(Y-T)
where Y is total income (GDP), G is the government expenditure, T are the taxes, C is
aggregate consumption that depends on disposable income (Y-T) and I is the
investment function that we assume to be negatively related with the interest rate (r).
a) Calculate private, public and national saving
b) Use the income expenditure identity to calculate the equilibrium interest rate
c) Now suppose that G increases to 4500, everything else constant. Calculate the
private, public and national saving in this case
d) Find the new equilibrium interest rate.
2.
Determine whether each of the following production functions has constant,
increasing, or decreasing returns to scale:
F(K,L)=2K + 15L
F(K,L)=  KL
F(K,L)=  2K 15L
3.
Which of the production functions in question 2 have diminishing marginal returns
to labor?
4.
[Optional] Assume that the production function is defined as Y=F(K, L) show, by
using Euler's theorem, that each factor input (K and L) is paid its marginal product under
the following assumptions: a) Constant returns to scale; b) Competitive markets.