let: y=14+2x1+x2-0.12x1-0.08x2+0.12x1x2 given: Py= $5/unit Px1=$1/unit Px2=$2/unit Fixed cost= $200 find a. the amount of (x1)...
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let: y=14+2x1+x2-0.12x1-0.08x2+0.12x1x2
given: Py= $5/unit
Px1=$1/unit
Px2=$2/unit
Fixed cost= $200
find
a. the amount of (x1)...
Let P = (Px, Py) be the point on the unit circle (given by x2+y2=1) in...
Let P = (Px, Py) be the point on the unit circle (given by x2+y2=1) in the first quadrant which maximizes the function f(x,y) = 4x+ y. Find Py?. Pick one of the choices O 1/5 O 1/9 O 1/13 O 1/17
(4) Consider rolling three dice. Let X1, X2, and X3 the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find the conditional PMF py)xi (yr) (b) Fi...
(4) Consider rolling three dice. Let X1, X2, and X3 the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find the conditional PMF py)xi (yr) (b) Find the probability that the maximum of all three dice is 4 given that the first die is a 3. (c) Find the probability that the maximum of all three dice is 3 given that the first die is a 3
(4) Consider...
(4) Consider rolling three dice. Let X1, X2, and X3 the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find the conditional PMF py)xi (yr) (b) Fi...
(4) Consider rolling three dice. Let X1, X2, and X3 the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find the conditional PMF py)xi (yr) (b) Find the probability that the maximum of all three dice is 4 given that the first die is a 3. (c) Find the probability that the maximum of all three dice is 3 given that the first die is a 3
(4) Consider...
A firm uses two inputs x1 and x2 to produce output y. The production function is...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
5. Let the firm's production function be given by y = x1 + x2. Note that the inputs 21 and 2 are perfect substitu...
5. Let the firm's production function be given by y = x1 + x2. Note that the inputs 21 and 2 are perfect substitutes in this production process. Suppose w = 2 and w2 = 1. (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price...
$ 200, if x > 10 else 3) Let X1, X2,..., X, bei.i.d. random variables from...
$ 200, if x > 10 else 3) Let X1, X2,..., X, bei.i.d. random variables from a population with f(x;0) = 0 > 0 being unknown parameter. a) Sketch a graph of a density from this family for a fixed 0. b) Find the cumulative distribution function F(x;0) of X1. c) Show that X (1) is a minimal sufficient statistic for e. 2n02n o d) Show that the density of X(1) is given by fx y2n +T, if y (y;0)...
Question 1: Let T: R3 ---> R2 defined by T(x1,x2,x3) = (x1 + 2x2, 2x1 - x2). Show that T as defined above is a Liner Transformation. Question 2: Determine whether the given set of vectors is a basi...
Question 1: Let T: R3 ---> R2 defined by T(x1,x2,x3) = (x1 + 2x2, 2x1 - x2). Show that T as defined above is a Liner Transformation. Question 2: Determine whether the given set of vectors is a basis for S = {(1,2,1) , (3,-1,2),(1,1,-1)} R3 Need answers to both questions.
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the...
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the consumer's Marshallian demand functions. (2) Find the consumer's compensated demand functions. (3) Suppose the price of good y is Py = $1 per unit and the consumer's income is 1 = $20. Find the total effects on good x and good y when the price of good x increases from px - $1 per unit to p} = $2 per unit.
Let X1 and X2 be two discrete random variables, where X1 can attain values 1, 2,...
Let X1 and X2 be two discrete random variables, where X1 can
attain values 1, 2, and 3, and X2 can attain values 2, 3 and 4. The
joint probability mass function of these two random variables are
given in the table below: X2 X1 2 3 4 1 0.05 0.04 0.06 2 0.1 0.15
0.2 3 0.2 0.1 0.1 a. Find the marginal probability mass functions
fX1 (s) and fX2 (t). b. What is the expected values of X1...
Let P = (Px, Py) be the point on the unit circle (given by x2+y2=1) in the first quadrant which maximizes the function f(x,y) = 4x+ y. Find Py?. Pick one of the choices O 1/5 O 1/9 O 1/13 O 1/17
(4) Consider rolling three dice. Let X1, X2, and X3 the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find the conditional PMF py)xi (yr) (b) Find the probability that the maximum of all three dice is 4 given that the first die is a 3. (c) Find the probability that the maximum of all three dice is 3 given that the first die is a 3
(4) Consider...
(4) Consider rolling three dice. Let X1, X2, and X3 the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find the conditional PMF py)xi (yr) (b) Find the probability that the maximum of all three dice is 4 given that the first die is a 3. (c) Find the probability that the maximum of all three dice is 3 given that the first die is a 3
(4) Consider...
A firm uses two inputs x1 and x2 to produce
output y. The production function is given by f(x1, x2) = p
min{2x1, x2}. The price of input 1 is 1 and the price of input 2 is
2. The price of output is 10.
4. A firm uses two inputs 21 and 22 to produce output y. The production function is given by f(x1, x2) = V min{2x1, x2}. The price of input 1 is 1 and the price...
5. Let the firm's production function be given by y = x1 + x2. Note that the inputs 21 and 2 are perfect substitutes in this production process. Suppose w = 2 and w2 = 1. (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price...
$ 200, if x > 10 else 3) Let X1, X2,..., X, bei.i.d. random variables from a population with f(x;0) = 0 > 0 being unknown parameter. a) Sketch a graph of a density from this family for a fixed 0. b) Find the cumulative distribution function F(x;0) of X1. c) Show that X (1) is a minimal sufficient statistic for e. 2n02n o d) Show that the density of X(1) is given by fx y2n +T, if y (y;0)...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the consumer's Marshallian demand functions. (2) Find the consumer's compensated demand functions. (3) Suppose the price of good y is Py = $1 per unit and the consumer's income is 1 = $20. Find the total effects on good x and good y when the price of good x increases from px - $1 per unit to p} = $2 per unit.
Let X1 and X2 be two discrete random variables, where X1 can
attain values 1, 2, and 3, and X2 can attain values 2, 3 and 4. The
joint probability mass function of these two random variables are
given in the table below: X2 X1 2 3 4 1 0.05 0.04 0.06 2 0.1 0.15
0.2 3 0.2 0.1 0.1 a. Find the marginal probability mass functions
fX1 (s) and fX2 (t). b. What is the expected values of X1...
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