Homework Answers
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s...
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s optimal consumption of good 1. (Hint: you can use the 5 step method or one of the demand functions derived in class to find the answer). 2.) Using the information from question 1, find Liz’s optimal consumption of good 2 3.) Lyndsay has utility given by u(x2,x1)=min{x1/3,x2/7}. If P1=$1, P2=$1, and I=$10, find Lyndsay’s optimal consumption of good 1. (Hint: this is Leontief utility)....
8. Consider the region bounded by the y = x2 - 2x + 1 and y...
8. Consider the region bounded by the y = x2 - 2x + 1 and y = 1 + 2x - x? Find the area of the region. a. b. Find the volume of the solid when the region is rotated about the x-axis. c. Find the volume of the solid when the region is rotated about the y-axis. d. Find the volume of the solid when the region is rotated about the line x = 5. e. If the...
uestion 3 (1 point) the production function is f(x1, x2) = x1/21x1/22. If the price of...
uestion 3 (1 point) the production function is f(x1, x2) = x1/21x1/22. If the price of factor 1 is $10 and the price of factor 2 is $20, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? Question 3 options: We can’t tell without knowing the price of output. x1 = 2x2. x1 = 0.50x2. x1 = x2. x1 = 20x2. Question 4 (1 point) A firm has the production function f(X,...
using the general power rule Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2...
using the general power rule
Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2 3(x2+x)2 (2x+1) • (x2+x)2 (2x+1) recall general power rule formula has three parts: [u(x)" ]' = n u(x)" 1 u'(x) Question 2 let y = (x3 +x2) 1/3 Find y' (x3 +x2) 1/3 (1/3) (x3 +x2) 1/3 . (1/3)(x3 +x2)-2/3 (1/3)(x3 +x2-2/3 (3x2+2x) recall general power rule has three parts. [u(x)"l' = n u(x)n-1 u'(x) Question 5 let g(x) = 1/(x3+x2)3 find g'(x) (x²+x23...
through tne po State the equation of the straight line parallel to the line y point...
through tne po State the equation of the straight line parallel to the line y point (-4, 5). 3x+ 7 and passing through the 3. Given the linear equations: 2y 3x - 7 2x 5-3y 2y 3x 8 Write the three equations in the form y=mx +c. Hence state: (a) which pair of straight lines are parallel (b) which pair of straight lines are perpendicular to each other. Prove your answer in each case.
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent p...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
(a) If C is the line segment connecting the point (X1,Y1) to the point (X2, y2),...
(a) If C is the line segment connecting the point (X1,Y1) to the point (X2, y2), find the following. e x dyr dy - y dx xly2 - x2y1 x A= A= (b) If the vertices of a polygon, in counterclockwise order, are (X1,Y1). (X2, y2), ..., (X, Yn), find the area of the polygon. [0x271 – 1/2) + (x392 – x2Y3) + .. + ... + (xnxn-1 - xn-1n) + (*11n – Xnxx)] + x2+1) + (x2y + x372)...
8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that...
8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that M. 1, that is, M, converges in probability to 1 as n o . - Show that n(1 - M.) Exp(1), that is, n(1 - M.) converges in distribution to an exponential r.v. with mean 1 as n .
What are the marginal utilities of x1 and x2 given the following utility functions, then find...
What are the marginal utilities of x1 and x2 given the following utility functions, then find the MRS: U(x1, x2) = 4 x1 + 8 x2 U(x1, x2) = (x1 + 2)(x2 + 1) Example. To find the marginal utility for x1, think about how a 1 unit increase in x1, keeping all else constant, will change the amount of utility U. Once you have the marginal utilities for both, you can calculate the MRS.
(1 point) Let X1 and X2 be a random sample of size n= 2 from the...
(1 point) Let X1 and X2 be a random sample of size n= 2 from the exponential distribution with p.d.f. f(x) = 4e - 4x 0 < x < 0. Find the following: a) P(0.5 < X1 < 1.1,0.3 < X2 < 1.7) = b) E(X1(X2 – 0.5)2) =
8. Consider the region bounded by the y = x2 - 2x + 1 and y = 1 + 2x - x? Find the area of the region. a. b. Find the volume of the solid when the region is rotated about the x-axis. c. Find the volume of the solid when the region is rotated about the y-axis. d. Find the volume of the solid when the region is rotated about the line x = 5. e. If the...
using the general power rule
Question 1 let y = (x2 +x)3 Find y' 2x+1 3(x2+x)2 3(x2+x)2 (2x+1) • (x2+x)2 (2x+1) recall general power rule formula has three parts: [u(x)" ]' = n u(x)" 1 u'(x) Question 2 let y = (x3 +x2) 1/3 Find y' (x3 +x2) 1/3 (1/3) (x3 +x2) 1/3 . (1/3)(x3 +x2)-2/3 (1/3)(x3 +x2-2/3 (3x2+2x) recall general power rule has three parts. [u(x)"l' = n u(x)n-1 u'(x) Question 5 let g(x) = 1/(x3+x2)3 find g'(x) (x²+x23...
through tne po State the equation of the straight line parallel to the line y point (-4, 5). 3x+ 7 and passing through the 3. Given the linear equations: 2y 3x - 7 2x 5-3y 2y 3x 8 Write the three equations in the form y=mx +c. Hence state: (a) which pair of straight lines are parallel (b) which pair of straight lines are perpendicular to each other. Prove your answer in each case.
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
(a) If C is the line segment connecting the point (X1,Y1) to the point (X2, y2), find the following. e x dyr dy - y dx xly2 - x2y1 x A= A= (b) If the vertices of a polygon, in counterclockwise order, are (X1,Y1). (X2, y2), ..., (X, Yn), find the area of the polygon. [0x271 – 1/2) + (x392 – x2Y3) + .. + ... + (xnxn-1 - xn-1n) + (*11n – Xnxx)] + x2+1) + (x2y + x372)...
8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that M. 1, that is, M, converges in probability to 1 as n o . - Show that n(1 - M.) Exp(1), that is, n(1 - M.) converges in distribution to an exponential r.v. with mean 1 as n .
(1 point) Let X1 and X2 be a random sample of size n= 2 from the exponential distribution with p.d.f. f(x) = 4e - 4x 0 < x < 0. Find the following: a) P(0.5 < X1 < 1.1,0.3 < X2 < 1.7) = b) E(X1(X2 – 0.5)2) =
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