(a) Let x1 and x2 be normal goods. Graphically, represent the effect of an increase in...

(a) Let x1 and x2 be normal goods. Graphically, represent the effect of an increase in the price level of x2. Show the Slutsky substitution and income effects on a clearly labelled diagram. (b) On a separate graph, show what would happen if x2 is now a Giffen good. Show the (Slutsky) substitution and income effects clearly and explain which effect outweighs the other. Note: For both parts x1 should be on the x-axis Assume the utility function to be a cobb Douglas function. Please note that you need to draw indifference curves to represent the optimal bundles.

Expert Solution

Rahul Sunny answered 8 months ago

Let X1 and X2 be independent standard normal variables X1 ∼ N(0, 1) and X2 ∼...

Let X1 and X2 be independent standard normal variables X1 ∼ N(0, 1) and X2 ∼ N(0, 1). 1) Let Y1 = X12 + X12 and Y2 = X12− X22 . Find the joint p.d.f. of Y1 and Y2, and the marginal p.d.f. of Y1. Are Y1 and Y2 independent? 2) Let W = √X1X2/(X12 +X22) . Find the p.d.f. of W.

Bilal’s utility function is U(x1; x2) = x1x2 (assume x1 and x2 are normal goods). The...

Bilal’s utility function is U(x1; x2) = x1x2 (assume x1 and x2 are normal goods). The price of good 1 is P1, the price of good 2 is P2, and his income is $m a day. The price of good 1 suddenly falls. (a)Represent, using a clearly labelled diagram, the hicks substitution effect, the income effect and the total effect on the demand of good 1. (b) On a separate diagram, represent using a clearly labelled diagram, the slutsky substitution...

: Let X1, X2, . . . , Xn be a random sample from the normal...

: Let X1, X2, . . . , Xn be a random sample from the normal distribution N(µ, 25). To test the hypothesis H0 : µ = 40 against H1 : µne40, let us define the three critical regions: C1 = {x¯ : ¯x ≥ c1}, C2 = {x¯ : ¯x ≤ c2}, and C3 = {x¯ : |x¯ − 40| ≥ c3}. (a) If n = 12, find the values of c1, c2, c3 such that the size of...

. Let X1, X2, . . . , Xn be a random sample from a normal...

. Let X1, X2, . . . , Xn be a random sample from a normal population with mean zero but unknown variance σ 2 . (a) Find a minimum-variance unbiased estimator (MVUE) of σ 2 . Explain why this is a MVUE. (b) Find the distribution and the variance of the MVUE of σ 2 and prove the consistency of this estimator. (c) Give a formula of a 100(1 − α)% confidence interval for σ 2 constructed using the...

Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution...

Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution with pdf f(x; θ) = (x/θ) * e^x^2/(2θ) for x > 0 (a) It can be shown that E(X2 P ) = 2θ. Use this fact to construct an unbiased estimator of θ based on n i=1 X2 i . (b) Estimate θ from the following n = 10 observations on vibratory stress of a turbine blade under specified conditions: 16.88 10.23 4.59 6.66...

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where X1 is normally distributed with a mean of 113 cm and a standard deviation of 5 cm, X2 is normally distributed with a mean of 245 cm and a standard deviation of 10 cm, and X3 is normally distributed with a mean of 98 cm and a standard deviation of 2 cm. 1. Find the mean perimeter of the trapezoid. 2. Suppose X1;X2; and...

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where X1 is normally distributed with a mean of 113 cm and a standard deviation of 5 cm, X2 is normally distributed with a mean of 245 cm and a standard deviation of 10 cm, and X3 is normally distributed with a mean of 98 cm and a standard deviation of 2 cm. 1. Find the mean perimeter of the trapezoid. 2. Suppose X1, X2,...

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that...

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that T is invertible. b)Find T inverse.

Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be...

Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be the income of the consumer, P1 and P2 the prices of good 1 and good 2, respectively. To simplify, normalize the price of good 1, that is P1 = £1. (a) Write down the budget constraint and illustrate the set of feasible bundles using a figure. (b) Suppose that m = £100 and that P2 = £10. Find the optimal bundle for the consumer....

Let X1, X2, … , Xn be a random sample from a normal population with zero...

Let X1, X2, … , Xn be a random sample from a normal population with zero mean and unknown variance σ^2 . Find the maximum likelihood estimator of σ^2

Question

(a) Let x1 and x2 be normal goods. Graphically, represent the effect of an increase in...

Solutions

Expert Solution

Related Solutions

Let X1 and X2 be independent standard normal variables X1 ∼ N(0, 1) and X2 ∼...

Bilal’s utility function is U(x1; x2) = x1x2 (assume x1 and x2 are normal goods). The...

: Let X1, X2, . . . , Xn be a random sample from the normal...

. Let X1, X2, . . . , Xn be a random sample from a normal...

Let X1, X2, . . . , Xn represent a random sample from a Rayleigh distribution...

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...

Let Y = X1 + X2 + 2X3 represent the perimeter of an isosceles trapezoid, where...

Let T(x1, x2) = (-x1 + 3x2, x1 - x2) be a transformation. a) Show that...

Let the utility function be given by u(x1, x2) = √x1 + x2. Let m be...

Let X1, X2, … , Xn be a random sample from a normal population with zero...