21. Bryan consumes only goods 1, 2, and 3 (in quantities x1,x2, and x3 respectively) and...
21. Bryan consumes only goods 1, 2, and 3 (in quantities x1x2,and x3 respectively) and as preferences over (x1, X2, X3) bundles that are captured by the utility function uB(x1,X2,Xy) When prices were P,,52 p,-46 an$120, Bryan chose to purchase the bundle (10,10, 10). How much good2 l Bryan choose to purchase at prices unit unit unit $8 $12 P = _ and I = $240? (Assume Bryan makes purchases so as to 1unit' maximize his utility. [If the answer...
19. If f(x, y, z) = 4x2 + 3xyz + 2y3z + Vz, find the value of °(3.) Y2) when x = 1, y=2, z= 3. дх 20. If u(x1, x2) = 18x1 + 3x2, find the value of MRS(8,13). (Don't forget to include a minus sign when entering your answer!) unit unit unit 21. Bryan consumes only goods 1, 2, and 3 (in quantities X1, X2, and xz respectively) and as preferences over (X1, X2, X3) bundles that are...
Problem 2 1. Bob consumes two types of goods. He thinks that a consumption bundle (xı, x2) is at least as good as a bundle (yı, y2) if and only if x1 2 y and x2 2 y2. Are his weak preferences complete? Reflexive? Transitive? 2. Randy hates studying both economics and history. The more time he spends studying either subject, the less happy he is. But Randy has strictly convex preferences. (a) Sketch an indifference curve for Randy where...
3. A consumer has a utility function defined over three goods, U(x1,x2,x3). At a given set of prices and income (p1,p2,p3), a. Can all three goods be necessities b. Can one good be inferior and the other two luxuries c. Find the income elasticity of good 1 if s2 = 0.2, s3 = 0.5, n2 = 2, and n3 = 1, where sj is the budget share of good j and nj is the income elasticity of good j.
Let X1,X2 and X3 be three discrete random variables withP[X1 = 0] = P[X1 = 1] = P[X2 = 0] = P[X2 = 1] = 1/2and P[X3 = 0] = 1.(i) Characterize all possible coupling between X1 and X2.(ii) Which coupling maximizes the correlation? Which coupling minimizes thecorrelation? Do you have an intuitive explanation why these couplings are theones that minimize/maximize the correlation?(iii) Which coupling makes the two random variables uncorrelated?(iv) Do the tasks (i) − (iii) but for X1...
Question 1: Louis the retired Canadian lives on a fixed budget and consumes only two goods: toques (T) and maple syrup (M). Suppose Louis monthly budget is 100 and the price of the two goods are (PT,PM) (4,2). (a) Make a properly labeled diagram illustrating Louis'budget constraint with T on the hori- zontal axis and M on the vertical axis. Indicate the area corresponding to the set of bundles (M, T) that Louis can afford. (b) What is the maximum...
23. Compute if x1=2, x2=5 and x3=0. 24. Compute ∑ i = 1 3 x i f i if x1=1, x2=3, x3=4 and f1=f2=2, f3=5. 25. Compute if x1=1, x2=3, x3=4 and f1=f2=2, f3=5.
number 1 please Problem 2. Consider a consumer has Cobb-Douglas preferences over two goods 21 and 22, given by u (21, 22) = 7 ln 21 + In 22. Let pı = 5 and p2 = 3 be the prices of the two goods, and suppose the agent has income I = 20. Suppose there is rationing of goods, so that in addition to paying for goods, the agent must have the appropriate number of coupons. Suppose, the agent begins...
Suppose you have a total income of I to spend on two goods x1 and x2, with unit prices p1 and p2 respectively. Your taste can be represented by the utility function u left parenthesis x subscript 1 comma x subscript 2 right parenthesis equals x subscript 1 cubed x subscript 2 squared (a) What is your optimal choice for x1 and x2 (as functions of p1 and p2 and I) ? Use the Lagrange Method. (b) Given prices p1...
Suppose that there two goods, X and Y , available in arbitrary nonnegative quantities (so the the consumption set is R 2 +). The consumer has preferences over consumption bundles that are monotone, strictly convex, and represented by the following (differentiable) utility function: u(x, y) = α √ x + (1 − α) √ y, where x is the quantity of good X, y is the quantity of good Y , and α ≥ 0 is a utility parameter. The...