PROBLEM 1
Decision maker (consumer) acts according To
his (subjective, individual) preferences
treating two goods as perfect substitutes
where the marginal rate of substitution of
a good X for good Y is constant
MRS(X,Y) = 3.
a) Find a functional form of utility representing
these preferences
b) Sketch the indifference curves map for it
c) Order in ascending order ("from the bottom
to the top")–according to them – baskets ,
which follow below:
A(2,5), B(1,6), C(3,5), D(3,6), E(10,5). Don’t
some of the lie on the same indifference
curve ? If so, what does it mean?
PROBLEM 2 Assume, that there are
constraints for consumer’s possibilities (
concerning buying), resulting from price
system and consumer’s income):
namely p x = 8, p y = 12, I = 144 :(p x x + p y y I).
Which of above baskets (from problem 1)
are available for him /her? Sketch the
corresponding budget set B.
PROBLEM 3
Let preferences R has representation by
utility function
u(x,y) = min(3x,y) (Koopmans-Leontief).
Assume the same budget set as in the
problem 2 (B). Determine the optimal basket
of goods (X,Y). Hint: "Optimal" - means ,
providing maximum satisfaction, measured by
utility function,
PROBLEM 4
Let production function be of Cobb-
Douglas form
U(x,y) = x y 3 . Calculate the values of marginal
productivities of capital (x) and labor (y) at the
point (X,Y) = (3,2)
please provide solutions with very
comprehensive justifications. This
will create an opportunity to
recognize that you understand (to
some extent) these issues, the
solutions sent are - perhaps - the
result of independent work, or at
least - conscious work.