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1 for good x2 5. Given the market prices p a consumer with U(x1, x2) income...
1) Optimization problem 1 Max U(x, y) = x1^0.5 + x2^0.5 s.t. x1 + x2...
1) Optimization problem 1 Max U(x, y) = x1^0.5 + x2^0.5 s.t. x1 + x2 =16 Find the optimum bundle; check if there is a minimum or a maximum. 2) Give the interpretation of the expenditure function, explain and show its properties. Draw the diagram of the expenditure function. Derive the compensated demand function for x1 and x2 E( p, u) = p(p1. p2)^0,5 and the uncompensated demand function. 3) Derive the expenditure function when the direct utility function...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes...
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given. > 1. What is special about P2 1) Find the demand functions for and x2 assuming these demand functions? Are both goods normal? Are these tastes homothetic? 2) Now find the demand functions for x1 and x2 assuming-<1. You probably P2 assumed the opposite above, so now will you find something different. Explain 3) Graph...
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...
1. (10 points) Market demand Part 1 There are two consumer goods, X1 and 22. Consumers all have income given by m, and...
1. (10 points) Market demand Part 1 There are two consumer goods, X1 and 22. Consumers all have income given by m, and a utility function U (x1, x2) = aln(x1) + ln(x2). The price of the two goods are pı and p2. (a) Find the individual demand functions for Xı and 22. (b) The parameter a differs across consumers. Type A consumers have a = 1. Type B consumers have a = 2. If there is one type A...
There are two consumer goods, xi and x2. Consumers all have income given by m, and a utility function U(, x2) = aln(x1)...
There are two consumer goods, xi and x2. Consumers all have income given by m, and a utility function U(, x2) = aln(x1)+In(x2). The price of the two goods are pi and p2 (a) Find the individual demand functions for x1 and r2 (b) The parameter a differs across consumers. Type A consumers have a = 1. Type B consumers have a = 2. If there is one type A person and two type B people, what is market demand...
A consumer has preferences represented by the utility function: u(21,12)=x2? Market prices are p1 = 2...
A consumer has preferences represented by the utility function: u(21,12)=x2? Market prices are p1 = 2 and P2 = 5. The consumer has an income m = 13. Find an expression for the consumer's demand for good 1,21 (P1). 39p1
A total income of I is given to spend on two goods x1 and x2 with...
A total income of I is given to spend on two goods x1 and x2 with prices p1 and p2 respectively. Your utility function for x1 and x2 is: U (x1, x2) = x13 x22 Using this information, solve the following questions: (a) Using the Lagrange Method, solve for your optimal choice for x1 and x2 as functions of p1 and p2 and I (b) What is the maximum utility you can attain given prices p1 and p2 with an...
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. Suppose that a consumer has a utility function U(x1,x2) = x0.5x0.5 . Initial prices are...
1. Suppose that a consumer has a utility function U(x1,x2) = x0.5x0.5 . Initial prices are P1=1 and P2 = 1, and income is m 100. Now, the price of good 1 increases to 2. (a) On the graph, please show initial choice (in black), new choice (in blue), compen- sating variation (in green) and equivalent variation (in red). (b) What is amount of the compensating variation? How to interpret it? (C) What is amount of the equivalent variation? How...
Suppose a consumer has a utility function U (x1,x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given 1) Find the demand functions for x1 and x2 assuming -> 1. What is special about Р2 these demand functions? Are both goods normal? Are these tastes homothetic? <1. You probably P2 2) Now find the demand functions for x1 and x2 assuming assumed the opposite above, so now will you find something different. Explain....
Suppose a consumer has a utility function U(x1, x2) = Inxi + x2. The consumer takes prices (p1 and p2) and income (I) as given. > 1. What is special about P2 1) Find the demand functions for and x2 assuming these demand functions? Are both goods normal? Are these tastes homothetic? 2) Now find the demand functions for x1 and x2 assuming-<1. You probably P2 assumed the opposite above, so now will you find something different. Explain 3) Graph...
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...
1. (10 points) Market demand Part 1 There are two consumer goods, X1 and 22. Consumers all have income given by m, and a utility function U (x1, x2) = aln(x1) + ln(x2). The price of the two goods are pı and p2. (a) Find the individual demand functions for Xı and 22. (b) The parameter a differs across consumers. Type A consumers have a = 1. Type B consumers have a = 2. If there is one type A...
There are two consumer goods, xi and x2. Consumers all have income given by m, and a utility function U(, x2) = aln(x1)+In(x2). The price of the two goods are pi and p2 (a) Find the individual demand functions for x1 and r2 (b) The parameter a differs across consumers. Type A consumers have a = 1. Type B consumers have a = 2. If there is one type A person and two type B people, what is market demand...
A consumer has preferences represented by the utility function: u(21,12)=x2? Market prices are p1 = 2 and P2 = 5. The consumer has an income m = 13. Find an expression for the consumer's demand for good 1,21 (P1). 39p1
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. Suppose that a consumer has a utility function U(x1,x2) = x0.5x0.5 . Initial prices are P1=1 and P2 = 1, and income is m 100. Now, the price of good 1 increases to 2. (a) On the graph, please show initial choice (in black), new choice (in blue), compen- sating variation (in green) and equivalent variation (in red). (b) What is amount of the compensating variation? How to interpret it? (C) What is amount of the equivalent variation? How...
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