1. Provide the formulas for the determining
optimal basket of (consumption, demanding)
2 goods, given the budget constraints
p x + p y I
for 3 basic kinds of preferences
A. When goods are perfect substitutes
(linear utility function u(x,y) =ax +by).
Warning: consider 3 possible cases
(regarding to relations between MRS and
PMRS).
B. When goods are perfect complements
(utility L-shaped function of Koopmans-
Leontief u(x,y) = min(ax,by)
C. For Cobb-Douglas (power) utility
function u(x,y) =
2. Determining an optimal inter-temporal
consumption allocation for two periods for
inter-temporal utility
A. U(c 1 , c 2 ) = a c 1 + bc 2 (a,b) = (2,3)
B. U(c 1 , c 2 ) = c 1 2 + c 2 3
and interest rate i = 25%.
and initial stream of resources (incomes
(Y 1 ,Y 2 ) = (30,60).
3. For Cobb-Douglas production function (of
capital K and labor L) F(K,L)= 5K 2 L 3
determine
A. the marginal productivities of production
factors (K and L)
B. The elasticity of F(K,L) with respect to
production factors (F(K,L)) and
(F(K,L))
4. For the simplified ( s.c "stylized", buy in the
same time, very important and illustrative)
demand function of two variables: price p
and income I)
D(p,I) =
calculate the price elasticity and income elasticity
(both- s.c. partial elasticities) factors D(p,I) and
D(p,I) .