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The following questions refer to the paf s below 1/3 Px(x) -2.5 0 2.5 0.75 py(y)...
1.2 (10 mks each). In parts a) and b) below, assume px = $1, py =...
1.2 (10 mks each). In parts a) and b) below, assume px = $1, py = $5, I = income = $21. Solve the U-max problem for each of the following two utility functions: (a) U = xy?, x, y = 0; (b) U=x1/3y2/3, x, y 2 0; (c) now, let px = p, Py = $5, 1 = $21, find the u-max solution for U = xy?, x, y = 0; (d) let px = 1, Py = p,...
(a) 1.2 (10 mks each). In parts a) and b) below, assume px = $1, Py...
(a) 1.2 (10 mks each). In parts a) and b) below, assume px = $1, Py = $5, I = income = $21. Solve the U-max problem for each of the following two utility functions: U= xy?, x, y 2 0; (b) U = x1/3y2/3, x, y = 0; now, let px = P, Py = $5, I = $21, find the u-max solution for U = xy?, x, y 2 0; let px = 1, Py =p, I =...
Given a utility function U(x,y) = xy. The price of x is Px, while the price of y is Py. The income is I. Suppose at period 0, Px = Py = $1 and income = $8. At period 1, price of x (Px) is changed to $4. Compute the price effect, substitution effect, and
Given a utility function U(x,y) = xy. The price of x is Px, while the price of y is Py. The income is I. Suppose at period 0, Px = Py = $1 and income = $8. At period 1, price of x (Px) is changed to $4. Compute the price effect, substitution effect, and income effect for good x from the price change.
QUESTION 7 If utility is given by Uxy)=x +y and px = 3, Py = 3,...
QUESTION 7 If utility is given by Uxy)=x +y and px = 3, Py = 3, 1 = 60, this person will choose: a. (10, 10). O b.(5, 15). Oc. (15,5). Od. either (0,20) or (20, 0).
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distributio...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer.
(20 points) Consider the following joint distribution of X and...
The demand for good X is given by QXd = 6,000 - (1/2)PX - PY +...
The demand for good X is given by QXd = 6,000 - (1/2)PX - PY + 9PZ + (1/10)M Research shows that the prices of related goods are given by Py = $6,500 and Pz = $100, while the average income of individuals consuming this product is M = $70,000. a. Indicate whether goods Y and Z are substitutes or complements for good X. Good Y is: (Click to select) a substitute neither complement nor substitute a complement . Good Z is: (Click to select) a complement a...
7. Let X and Y have joint pdf 122 (1-x)y, 0, 0〈x〈1,0くyく1. otherwise. x,y(x,y) = (a) Find the joint cdf of X and Y. (4pts) (b) Find PY< VX. (Spts) (c) Find the marginal pdfs of X and Y. (6pts)...
7. Let X and Y have joint pdf 122 (1-x)y, 0, 0〈x〈1,0くyく1. otherwise. x,y(x,y) = (a) Find the joint cdf of X and Y. (4pts) (b) Find PY< VX. (Spts) (c) Find the marginal pdfs of X and Y. (6pts) (d) Are X and Y independent? (5pts)
7. Let X and Y have joint pdf 122 (1-x)y, 0, 0〈x〈1,0くyく1. otherwise. x,y(x,y) = (a) Find the joint cdf of X and Y. (4pts) (b) Find PY
H(X) means entropy of X. I have some questions when solving this problem. (a) Refer to...
H(X) means entropy of X.
I have some questions when solving this problem.
(a) Refer to similar questions, H(Z|X)=H(Y|X) if Z=X+Y， I want
to know whether we can simplify H(X|Z)?
(b) if Px(X=0)=0.5, Px(X=1)=0.5, Py(Y=0)=0.5, Py(Y=-1)=0.5, if
they are not independent, can I just give random variable Z with
its probability distribution as P(Z=0)=1, P(Z=1)=0, P(Z=-1)=0.
(c)Plus, I also want to know the answer to the original problem
with 4 questions.
Let X and Y be two random variables defined...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her i...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her income I = 10. (e) Draw an optimal bundle which is the result of utility maximization under given budget set. (Hint: Assume interior solution). Define corresponding expenditure minimization problem (note the elements for expenditure minimization problem are (i) objective function, (ii) constraint, (iii) what to choose). (f)Describeaboutwhatthedualityproblemis. Definemarshalliandemandfuction andhicksiandemandfunction. (Hint: identifytheinputfactorsofthesefunctions.) (g) Consider a price increase for the good x from...
2. The annual market own-price demand function for good X is estimated as X=142-5PX-1 -3.5 Py...
2. The annual market own-price demand function for good X is estimated as X=142-5PX-1 -3.5 Py where X quantity demanded of good X in units/year Px = price of good X in dollars/unit per capita income in dollarsyear Py price of good Y in dollars/unit a) Calculate the market (own-price) demand curve when I = 25 and Py =12 b) Using your results from part a), calculate the quantity of good X demanded in the market when PX-10 c) Calculate...
1.2 (10 mks each). In parts a) and b) below, assume px = $1, py = $5, I = income = $21. Solve the U-max problem for each of the following two utility functions: (a) U = xy?, x, y = 0; (b) U=x1/3y2/3, x, y 2 0; (c) now, let px = p, Py = $5, 1 = $21, find the u-max solution for U = xy?, x, y = 0; (d) let px = 1, Py = p,...
(a) 1.2 (10 mks each). In parts a) and b) below, assume px = $1, Py = $5, I = income = $21. Solve the U-max problem for each of the following two utility functions: U= xy?, x, y 2 0; (b) U = x1/3y2/3, x, y = 0; now, let px = P, Py = $5, I = $21, find the u-max solution for U = xy?, x, y 2 0; let px = 1, Py =p, I =...
QUESTION 7 If utility is given by Uxy)=x +y and px = 3, Py = 3, 1 = 60, this person will choose: a. (10, 10). O b.(5, 15). Oc. (15,5). Od. either (0,20) or (20, 0).
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer.
(20 points) Consider the following joint distribution of X and...
7. Let X and Y have joint pdf 122 (1-x)y, 0, 0〈x〈1,0くyく1. otherwise. x,y(x,y) = (a) Find the joint cdf of X and Y. (4pts) (b) Find PY< VX. (Spts) (c) Find the marginal pdfs of X and Y. (6pts) (d) Are X and Y independent? (5pts)
7. Let X and Y have joint pdf 122 (1-x)y, 0, 0〈x〈1,0くyく1. otherwise. x,y(x,y) = (a) Find the joint cdf of X and Y. (4pts) (b) Find PY
H(X) means entropy of X.
I have some questions when solving this problem.
(a) Refer to similar questions, H(Z|X)=H(Y|X) if Z=X+Y， I want
to know whether we can simplify H(X|Z)?
(b) if Px(X=0)=0.5, Px(X=1)=0.5, Py(Y=0)=0.5, Py(Y=-1)=0.5, if
they are not independent, can I just give random variable Z with
its probability distribution as P(Z=0)=1, P(Z=1)=0, P(Z=-1)=0.
(c)Plus, I also want to know the answer to the original problem
with 4 questions.
Let X and Y be two random variables defined...
2. The annual market own-price demand function for good X is estimated as X=142-5PX-1 -3.5 Py where X quantity demanded of good X in units/year Px = price of good X in dollars/unit per capita income in dollarsyear Py price of good Y in dollars/unit a) Calculate the market (own-price) demand curve when I = 25 and Py =12 b) Using your results from part a), calculate the quantity of good X demanded in the market when PX-10 c) Calculate...
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