1. A buyer has Cobb-Douglas preferences such that mrs = − x2/ x1 . He starts...
1. A buyer has Cobb-Douglas preferences such that mrs = − x2/ x1 . He starts with 3 units of good 1 and $50. Use this information to answer the following questions.
(a) Find an expression for this consumer’s net demand for good 1 (i.e. how many more units he will buy given price p).
(b) Sketch this demand curve. (Make sure you label the axes and put p on the vertical axis.)
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1. A buyer has Cobb-Douglas preferences such that mrs = − x2/ x1
. He starts...
10. Omar has Cobb Douglas preferences for Juice (X1) and Soda (X2). His MRS at his...
10. Omar has Cobb Douglas preferences for Juice (X1) and Soda (X2). His MRS at his optimal consumption is 2. If the price of juice is p1= $6. What is the price of Soda, p2?
Please do all the parts and explain it well Priya has Cobb Douglas preferences for Juice...
Please do all the parts and explain it well Priya has Cobb Douglas preferences for Juice (X1) and Soda (X2). Her MRS at his optimal consumption is 2. If the price of juice is p1= $6. What is the price of Soda, p2?
Benjamin spends his time either watching movies (x1) (he uses "on demand" option, cable TV) or li...
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 =...
Suppose a consumer has quasi-linear utility: u(x1, x2) = 3.01 + x2. The marginal utilities are...
Suppose a consumer has quasi-linear utility: u(x1, x2) = 3.01 + x2. The marginal utilities are MU(X) = 2x7"! and MU2:) = 1. Throughout this problem, assume P2 = 1. (a) Sketch an indifference curve for these preferences (label axes and intercepts). (b) Compute the marginal rate of substitution. (c) Assume w> . Find the optimal bundle (this will be a function of pı and w). Why do we need the assumption w> (d) Sketch the demand function for good...
Assume John has Cobb-Douglas utility function for bread (B) and whiskey (W): U= 2 BSWS Marginal...
Assume John has Cobb-Douglas utility function for bread (B) and whiskey (W): U= 2 BSWS Marginal utilities are as followed: MUB=B-05W. and MUw = 30.5W-0.5 a. Write down the expression for MRSow (i.e., you need to simplify the ratio and come up with a neat result) b. What is MRSBw at bundle A(4,4)? At bundle B(1,16)? C. Regarding MRSBw, we consider a movement along an indifference curve from the left to the righ (getting more of bread, the good on...
The utility function is u = x1½ + x2, and the budget constraint is m =...
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...
1 pts Question 2 A consumer has preferences represented by the utility function: u(x1, x2)= x...
1 pts Question 2 A consumer has preferences represented by the utility function: u(x1, x2)= x x Market prices are pi = 3 and P2 = 4. The consumer has an income m 30. Find an expression for the consumer's Engel curve for good 1. x1(m). ооо D Question 3 1 pts
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min...
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
Person A and B both have Cobb-Douglas preferences, uA = (x1A)2/5 · (x2A)3/5and uB = x1B...
Person A and B both have Cobb-Douglas preferences, uA = (x1A)2/5 · (x2A)3/5and uB = x1B · x2B . Their endowments are wA = (0, 2) and wB = (4, 0). Find their demand functions and use market clearing to derive equilibrium price for good two, p2 (set p1=1, and enter your answer as a simplified decimal). Solve for the contract curve for the setting described in question 1.). Please write out its equation in the space below.
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗...
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗ = m/Px (a/a+b) where m is income and Px is the price of good x. Using this demand function, find the formula for this consumer’s price elasticity of demand. Interpret it in words.
Suppose a consumer has quasi-linear utility: u(x1, x2) = 3.01 + x2. The marginal utilities are MU(X) = 2x7"! and MU2:) = 1. Throughout this problem, assume P2 = 1. (a) Sketch an indifference curve for these preferences (label axes and intercepts). (b) Compute the marginal rate of substitution. (c) Assume w> . Find the optimal bundle (this will be a function of pı and w). Why do we need the assumption w> (d) Sketch the demand function for good...
Assume John has Cobb-Douglas utility function for bread (B) and whiskey (W): U= 2 BSWS Marginal utilities are as followed: MUB=B-05W. and MUw = 30.5W-0.5 a. Write down the expression for MRSow (i.e., you need to simplify the ratio and come up with a neat result) b. What is MRSBw at bundle A(4,4)? At bundle B(1,16)? C. Regarding MRSBw, we consider a movement along an indifference curve from the left to the righ (getting more of bread, the good on...
1 pts Question 2 A consumer has preferences represented by the utility function: u(x1, x2)= x x Market prices are pi = 3 and P2 = 4. The consumer has an income m 30. Find an expression for the consumer's Engel curve for good 1. x1(m). ооо D Question 3 1 pts
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
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