how did they dervice that to get 1/x1=p1/p2 income goes entirely to the consumption of good 2. If quasilinear,...
hi there! how did they get thst equation x1=am/p1? i dont know understand this paragraph. if someone could help that would be great! Cobb-Douglas Preferences For the case of Cobb-Douglas preferences it is easier to look at the algebraic! form of the demand functions to see what the graphs will look like. If u(11,12) = rm-9, the Cobb-Douglas demand for good 1 has the form 2 = am/pi. For a fixed value of Pı, this is a linear function of...
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)....
Suppose a consumer's optimal consumption of a good is determined by the equation x1 = x1(P1, P2, m) where P1 is the price of good 1, P2 is the price of good 2, and m is the consumer's income. If Əx1 > 0 Әрі which of the following must be true? Good 1 is an inferior good Good 1 is a normal good Good 1 and good 2 are substitutes Good 1 and good 2 are complements
A consumer has income M, and faces prices (for goods 1 and 2) p1 and p2. For each of the following utility functions, graphically show the following: (i) the Slutsky substitution and income e⁄ects when p1 decreases. (ii) the Hicks substitution and income e⁄ects when p1 decreases. (iii) the Marshallian and Hicksian demand curves for good 1: (a) perfect complements: U(x1 , x2) = min {4x1, 5x2} (b) quasi-linear: U(x1 , x2) = x^2/3 1 + x2
Suppose an individual’s utility function is u=x11/2, x21/2. Let p1=4, p2=5, and income equal $200. With a general equation and general prices, derive the equal marginal principle. Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility. What is the optimal amount of x1 consumed? What is the optimal amount of x2 consumed? What is the marginal rate of substitution at the optimal amounts of x1 and x2? As functions of p1, p2, and...
The utility function is u = x1½ + x2, and the budget constraint is m = p1x1 + p2x2. Derive the optimal demand curve for good 1, x1(p1, p2), and good 2, x2(m, p1, p2). Looking at the cross price effects (∂x1/∂p2 and ∂x2/∂p1) are goods x1 and x2 substitutes or complements? Looking at income effects (∂x1/∂m and ∂x2/∂m) are goods x1 and x2 inferior, normal or neither? Assume m=100, p1=0.5 and p2=1. Using the demand function you derived in...
Benjamin spends his time either watching movies (x1) (he uses "on demand" option, cable TV) or listening to songs - MP3 downloaded from the Internet (x2) . His preferences are described by U(x1,x2) = ln(x1) + ln(x2) a) Derive Benjamin's demand for movies and MP3 files as a function of prices p1,p2, and his income m. (do not use Cobb Douglas formula but rather derive demand using "two secrets of happiness"). b) Fix the price of MP3 at p2 =...
Margaret spends all of her income on t-shirts (x1) and shoes (x2). Her preferences can be represented by the utility function u (x1, x2) = 2√x1x2 (a) [15 Points] Derive the demand functions for t-shirts and shoes in terms of the price of t-shirts (p1), the price of shoes (p2), and income (m). Show your result on a graph. (b) [10 Points] Draw the Income Offer Curve and Engel Curves (one for each good). (c) [10 Points] Draw the Price...
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2, B) and x (P1, P2, B), and calculate 11 (income elasticity of good 1), €1 (own-price elasticity of good 1), and €12 (cross-price elasticity). a U(x1, x2) = 21 b U(x1, x2) = 2.925-a for a € (0,1) CU(21, 12) = ln(21) + x2 where B > P2.
Suppose a consumer's optimal consumption of a good is determined by the equation x* = x1(P1, P2, m) where p1 is the price of good 1, p2 is the price of good 2, and m is the consumer's income. If which of the following must be true? (Choose the best answer). O Good one and good 2 are complements Good 1 is not an inferior good O Good 1 is a Giffen good O Good one and good 2 are...