In: Economics

Will Smith consumes chocolate and milk. Let y denote chocolate
and x denote milk. Chocolate has an unusual market where there is
only one supplier, and the more chocolate you buy from the
supplier, the higher the price she charges per unit. In fact,
*y* units of chocolate will cost Will *y*^{2}
dollars. Milk is sold in the usual way at a price of 2 dollars per
unit. Will’s income is 20 dollars and his utility function is
*U* = *x* + 2*y*. Draw Will’s budget set and
shade it in. Sketch some of his indifference curves and label the
point that he chooses. Calculate the amount of milk and the amount
of chocolate that Will demands given these prices and this
income.

You roll two fair dice, and denote the number they show by X and
Y. Let U = min{X, Y } and V = max{X, Y }. Write down the joint
probability mass function of (U, V ) and compute ρ(U, V ) i.e the
correlation coefficient of U and V

Let X and Y denote the tarsus lengths of female and
male grackles, respectively. Assume normal distributions for X and
Y. Independent samples are selected from these populations and
suppose
n X = 17
x ¯ = 32
s X = 7
n Y = 12
y ¯ = 34
s Y = 6
Test at 5% significance level whether the true mean tarsus
length of female grackles is smaller than that of male grackles.
What is the rejection region...

Let X = NN endowed with the product topology. For x ∈
X denote x by (x1, x2, x3, . .
.).
(a) Decide if the function given by d : X × X → R is a metric on
X where, d(x, x) = 0 and if x is not equal to y then d(x, y) = 1/n
where n is the least value for which xn is not equal to
yn. Prove your answer.
(b) Show that no...

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}.
a) Prove or disprove: A ⊆ X
b) Prove or disprove: X ⊆ A
c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y )
d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )

Let Y denote a random variable that has a Poisson
distribution with mean λ = 6. (Round your answers to three
decimal places.)
(a) Find P(Y = 9).
(b) Find P(Y ≥ 9).
(c) Find P(Y < 9).
(d) Find P(Y ≥
9|Y ≥ 6).

Let T denote the counterclockwise rotation through 60 degrees,
followed by reflection in the line y=x
(i) Show that T is a linear transformation.
(ii) Write it as a composition of two linear
transformations.
(iii) Find the standard matrix of T.

Jen likes x but does not like y. For every y he consumes he has
to be compensated with ½ x.
Draw the indifference curves. Is there a budget constraint?

Let M(x, y) be "x has sent y an e-mail message" and T(x, y) be "
x has telephoned y, " where the domain consists of all students in
your class. Use quantifiers to express each of these
statements.
g. There is a student in your class who sent every one else in
your class an email message.
I answer ∃x( x ≠ y ∧ ∀? M (x, y) )
But answer on text book is ∃x( x ≠ y → ∀?...

Let ∬[a,b]×[c,d]f(x,y)dA denote the integral of f(x,y)over the
region with a≤x≤b and c≤y≤d. Find ∬[0,1]×[0,1]f(x,y)dA given the
following: ∬[0,1]×[1,5]f(x,y)dA=2, ∬[1,2]×[0,1]f(x,y)dA=−1,
∬[1,2]×[1,5]f(x,y)dA=4, and ∬[0,2]×[0,5]f(x,y)dA=3.
Group of answer choices
2
-2
8
0
None of the above.

A consumes two goods, x and y. A ’s utility function is given
by u(x, y) = x 1/2y 1/2
The price of x is p and the price of y is 1. A has an income
of M.
(a) Derive A ’s demand functions for x and y.
(b) Suppose M = 72 and p falls from 9 to 4. Calculate the
income and substitution effects of the price change.
(c) Calculate the compensating variation of the price
change....

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