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Question 3: Suppose there are two people in town. Their individual demands are given by Q4...
Given the following utility function: Where, q1 and q2 are consumer goods and the budget constraint...
Given the following utility function:
Where, q1 and q2 are consumer goods and the budget
constraint is given as.
With p, and p the prices of the goods and the month
the income. Find.
1. The Marshallian Demands for (q1 and 92.
2. The Indirect Utility Function, V (p1, p2, m)
3. The Hicksian Demands for q1 and q2.
4. The Expenditure Function, m (p1, p2, U)
U(992)=9, +10 log2 U(992)=9, +10 log2
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2.The prices of x1 and x2 are denoted as p1 and p2, and his income is m. 1. Draw at least three indifference curves and find its slope (i.e. MRS). Is the MRS changing depending on the points of (x1, x2) at which it is evaluated, or constant? 2. Draw a budget constraint assuming that p1 < P2. Find the optimal bundle (x1*,x2*) as a function of income and prices. 3....
This table contains prices and the demands of a consumer whose behavior was observed in 5...
This table contains prices and the demands of a consumer whose behavior was observed in 5 different price-income situations. Situation P1 P2 X1 X2 A 2 2 10 70 B 2 4 70 20 C 2 2 20 30 D 6 2 10 30 E 2 4 20 20 A. Sketch each of his budget lines and label the point chosen in each case by the letters A, B, C, D, and E. B. Is the consumer’s behavior consistent with...
α1-α Given prices (P1 and p2) and income (Y), we know from lecture that if preferences...
α1-α Given prices (P1 and p2) and income (Y), we know from lecture that if preferences can be represented by the Cobb-Douglas utility function u (q1,22 for 0< α< 1, then the demand for goods 1 and 2 are (1-a)Y P2 q1-- and q2 = P1 We also know that any monotonic transformation of utility represents the same preferences. Consider the monotonic transformation v (q1.q2,-In(u (442),-InG In q192 qq As was shown in lecture, by the rules of logarithms this...
how to solve this?! Section III Longer Problems (4 points each - 68 points total). Show your work. 1. Consider Mar...
how to solve this?!
Section III Longer Problems (4 points each - 68 points total). Show your work. 1. Consider Mary's utility function u(x1, +2) = [min{2x1, x2}]} (a) Draw Mary's indifference curve that yields u = 1 and u = 2. Mark the kink clearly. (b) Derive Mary's optimal demand function for each of the goods, i.e., find ai (P. P. m) and (P1, P2, m). (C) If Pi = 1, P2 = 1 and m 6, what is...
Each individual consumer takes the prices as given and chooses her consumption bundle, (r, 2) R, by maximizing...
Each individual consumer takes the prices as given and chooses her consumption bundle, (r, 2) R, by maximizing the utility function U (r1, T)= In(xr2), subject to the budget constraint pi 1 + p2 2 900 (a) (3 points) Write out the Lagrangian function for the consumer's problem (b) (6 points) Write out the system of first-order conditions for the consumer's problem (e) (6 points) Solve the system of first-order conditions to find the optimal values of r and r2....
Assume that a consumer’s preferences are given by u(x1, x2) = 10x11/2 * x21/2 Currently, m = 200 and p1 = 10...
Assume that a consumer’s preferences are given by u(x1, x2) = 10x11/2 * x21/2 Currently, m = 200 and p1 = 10 and p2 = 20. Suppose now that p1 increases to p'1 = 20. What is the total effect of this price change in the optimal consumption of the two goods for the consumer, and what are the substitution and income effects? Step 1:Solve the consumer’s problem given her preferences (described by u) and under the assumptions that m =...
Textbook: Nicholson & Snyder, Microeconomic Theory, 12th edition. In Problems 5 - 7, you are given...
Textbook: Nicholson & Snyder, Microeconomic Theory, 12th
edition.
In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices Prpy and final prices p., For each problem, you are to find: (a) the optimal choice at the initial prices b) i-he opi.İnnaal choice al the final prices (c) the change optimal choice at final prices-optimal choice at initial prices 7) u(r, y)-y4,1-12 p1.py-2 1,p 4 1/4,,3/4
8. Edna's preferences over romantic comedes zı and horror flicks z2 is given by u =エ122,...
8. Edna's preferences over romantic comedes zı and horror flicks z2 is given by u =エ122, which implies MU = z2 and MUr2 = zł. The prices of each are P1 and P2 per movie. Edna's monthly budget for movies is n (a) Solve algebraically for Edna's ordinary demand for romantic comedies P,2,) and for horror flicks = z2(P1,P2, m). The equations to be solved include丑= PL and m = p12 1 +P2X2. エ1 l mark (b) Evaluate these at...
4. An individual has preferences over two goods (x and y) that are represented by function...
4. An individual has preferences over two goods (x and y) that are represented by function U = min{x,y}. The individual has income $60, the price of x is $4 and the price of good y is $2. (a) What kind of goods are these to the individual? (i.e. what "special case” is this?) (b) What is this individual's budget constraint? (c) What is this individual's optimal bundle of x and y? [HINT: You can't take the derivative of this...
Given the following utility function:
Where, q1 and q2 are consumer goods and the budget
constraint is given as.
With p, and p the prices of the goods and the month
the income. Find.
1. The Marshallian Demands for (q1 and 92.
2. The Indirect Utility Function, V (p1, p2, m)
3. The Hicksian Demands for q1 and q2.
4. The Expenditure Function, m (p1, p2, U)
U(992)=9, +10 log2 U(992)=9, +10 log2
α1-α Given prices (P1 and p2) and income (Y), we know from lecture that if preferences can be represented by the Cobb-Douglas utility function u (q1,22 for 0< α< 1, then the demand for goods 1 and 2 are (1-a)Y P2 q1-- and q2 = P1 We also know that any monotonic transformation of utility represents the same preferences. Consider the monotonic transformation v (q1.q2,-In(u (442),-InG In q192 qq As was shown in lecture, by the rules of logarithms this...
how to solve this?!
Section III Longer Problems (4 points each - 68 points total). Show your work. 1. Consider Mary's utility function u(x1, +2) = [min{2x1, x2}]} (a) Draw Mary's indifference curve that yields u = 1 and u = 2. Mark the kink clearly. (b) Derive Mary's optimal demand function for each of the goods, i.e., find ai (P. P. m) and (P1, P2, m). (C) If Pi = 1, P2 = 1 and m 6, what is...
Each individual consumer takes the prices as given and chooses her consumption bundle, (r, 2) R, by maximizing the utility function U (r1, T)= In(xr2), subject to the budget constraint pi 1 + p2 2 900 (a) (3 points) Write out the Lagrangian function for the consumer's problem (b) (6 points) Write out the system of first-order conditions for the consumer's problem (e) (6 points) Solve the system of first-order conditions to find the optimal values of r and r2....
Textbook: Nicholson & Snyder, Microeconomic Theory, 12th
edition.
In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices Prpy and final prices p., For each problem, you are to find: (a) the optimal choice at the initial prices b) i-he opi.İnnaal choice al the final prices (c) the change optimal choice at final prices-optimal choice at initial prices 7) u(r, y)-y4,1-12 p1.py-2 1,p 4 1/4,,3/4
8. Edna's preferences over romantic comedes zı and horror flicks z2 is given by u =エ122, which implies MU = z2 and MUr2 = zł. The prices of each are P1 and P2 per movie. Edna's monthly budget for movies is n (a) Solve algebraically for Edna's ordinary demand for romantic comedies P,2,) and for horror flicks = z2(P1,P2, m). The equations to be solved include丑= PL and m = p12 1 +P2X2. エ1 l mark (b) Evaluate these at...
4. An individual has preferences over two goods (x and y) that are represented by function U = min{x,y}. The individual has income $60, the price of x is $4 and the price of good y is $2. (a) What kind of goods are these to the individual? (i.e. what "special case” is this?) (b) What is this individual's budget constraint? (c) What is this individual's optimal bundle of x and y? [HINT: You can't take the derivative of this...
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