Re: Micro
Posted by arpita lahiri on
URL: http://discussion-forum.276.s1.nabble.com/Micro-tp5202707p5208839.html
1. Consider a random variable X which can take only non zero integer values from -20 to +20, and
whose probability distribution is symmetric around 0. Suppose the function f(x), called the
probability mass function of X, gives the probability that X = x, ? x = -20,…,-1, 1, ….,20. Now
consider the random variable Y = max{X, -X}. Which of the following would be an appropriate
definition for g(y), the probability mass function for Y?
a) g(y) = max{f(y), f(-y)} ? y = 1, 2, …..,20 and g(y) = 0 otherwise.
b) g(y) = 2f(y) ? y = 1, 2, …..,20 and g(y) = 0 otherwise.
c) g(y) =f(max{y, -y}) ? y = 1, 2, …..,20 and g(y) = 0 otherwise.
d) None of the above
2. Consider an exchange economy with persons 1 and 2 and goods x and y. Person 1’s utility
x
function is u1(x, y) = min{x, y} and u2(x, y) = e . The total endowment of the economy is (2,1).
Which of the following is true about this economy?
a) All feasible allocations are efficient
b) Only allocations on the diagonal from 1’s origin to 2’s origin is efficient
c) Only allocations on the four boundaries of the edgeworth box are efficient
d) None of the above
3. Consider the situation of the preceding question. If person 1’s endowment is (1, 1) and 2’s
endowment is (1, 0), then the following allocation is a competitive equilibrium
a) (x1, y1) = (1, 1) (x2, y2) = (1, 0)
b) (x1, y1) = (1, 0) (x2, y2) = (1, 1)
c) (x1, y1) = (1.5, 0.5) (x2, y2) = (0.5, 0.5)
d) None of the above
4. Consider the situation of the preceding question. Which of the following is(are) equilibrium price
vectors?
a) (px, py) = (8/13, 5/13)
b) (px, py) = (1/2, 1/2)
c) (px, py) = (1, 0)
d) All of the above
5. Duopolists producing substitute goods q1 and q2 face inverse demand schedules:
p1 = 18 + (½) p2 – q1
And
p2 = 18 + (½) p1 – q2
respectively. Firm1 has marginal cost c and no fixed costs. Firm 2 has no costs. Each firm is a
cournot competitor in price, not quantity. Compute the cournot equilibrium in this market, giving
equilibrium price for each good. (Hint: Write the profit functions of two firms as a function of p1
and p2 and not quantities then compute the cournot equilibrium)
a) (p1, p2) = (12+8c/15, 12+2c/15)
b) (p1, p2) = (12+2c/15, 12+6c/15)
c) (p1, p2) = (12, 12)
d) None of the above
1 Definition 1: Relation between a set S and a set T is a subset of the Cartesian produc
In particular, a relation on a set S is a subset of S X S.
A binary relation R on the set S is formally defined as a subset of S X S – write R ?
and (x, y) ? R if the ordered pair (x, y) is in relation R. Another way to write (x, y) ?
Illustrations: Suppose S = {1, 2, 3}, given below are some examples of relations on S
R1 = {{1,2), (2,2), (2,3)}
R2 = {(1,1), (2,3)}
R3 = = defined as (x, y) ? R3 iff x = y.
Hence R3 = {(1,1), (1,2), (1,3), (2,2), (2,3), (3,3)}
Definition 2:
(a) Reflexivity: ? x ? S : (x, x) ? R
(b) Completeness: ? x, y ? S : x ? y ? (x, y) ? R or (y, x) ? R
(c) Transitivity: ? x, y, z ? S : ((x, y) ? R & (y, z) ? R) ? (x, z) ? R
(d) Symmetry: ? x, y ? S : (x, y) ? R ? (y, x) ? R
(e) Anti-symmetry: ? x, y ? S : ((x, y) ? R & (y, x) ? R) ? x = y
(f) Asymmetry: ? x, y ? S: (x, y) ? R ? (y, x) ? R
Consider the relation < on (strictly less than) where is the set of integers. WhicZ Z
following is true?
a) Relation < is reflexive and complete.
b) Relation < is transitive, symmetric and complete.
c) Relation < is transitive, complete, asymmetric and anti-symmetric.
d) Relation < is transitive, symmetric and asymmetric.
how 2 get the ans