Homework Answers
The demand function can be calculated by using the Optimality condition i.e. MRS = Price Ratio.
The market demand for any good is the sum of the individual demands.
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1. (10 points) Market demand Part 1 There are two consumer goods, X1 and 22. Consumers all have income given by m, and...
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...
1 for good x2 5. Given the market prices p a consumer with U(x1, x2) income...
1 for good x2 5. Given the market prices p a consumer with U(x1, x2) income $300. Now the price of good x changes. Find the uncompensated and compensated demand for good x 2 for good xı and p2 4x152i maximizing her utility with her
Assume that a person's utility over two goods is given by U(x1, x2) = (x1 −...
Assume that a person's utility over two goods is given by U(x1, x2) = (x1 − 10)^1/3 (x2 − 5)^2/3 The price of good x1 is equal to p1 and the price of good x2 is p2. The total income of the individual is given by I. (a) Write down the budget constraint of this person. (b) Calculate the demand for each one of the two goods. (c) Calculate the elasticity of demand for each one of the two goods.
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...
The market for good X consists of 2 consumers. Consumer 1’s demand for good X is:...
The market for good X consists of 2 consumers. Consumer 1’s demand for good X is: X1 = 15 - 3PX + 0.5PY + .02 *I1 Consumer 2's demand for X is: X2 = 10 - PX + 0.2PY + .01*I2 I1 and I2 are incomes of consumer 1 and 2, respectively. PX and PY are the prices of goods X and Y, respectively. a. What is the equation for the market demand function for X? Graph the two individual...
A consumer has income M, and faces prices (for goods 1 and 2) p1 and p2....
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
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 +...
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 + x2. a) Let pı = 2 ,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p1 = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1, p2 = 4 and m = 4. Compared to point b),...
4. General Equilibrium An economy consists of two consumers, indexed by j = A, B, who...
4. General Equilibrium An economy consists of two consumers, indexed by j = A, B, who consume two goods x, and x2. The first consumer's endowment of the two goods is (W1,W4) = (2,4), and the second consumer's endowment is (w,w) = (5,1), where w/ denotes consumer j's endowment of good i. a. Suppose the preferences of the two consumers are described by the utility functions U,(x) = (x^)(x4)4 and U2(x) = xPx, where x denotes consumer j's consumption of...
Consider the following function: where x1 2 0,0,A 0, 0<1. a) Suppose that the preferences of...
Consider the following function: where x1 2 0,0,A 0, 0<1. a) Suppose that the preferences of a consumer regarding the consumption of goods x1 and x2 are represented by function = f(x1,x2) above. Suppose also that the consumer is endowed with some disposable income Y > 0 and faces prices pı and p2 respectively for goods x1 and x2. i) Derive and describe the demand of the consumer for goods x1 and x2. [20 marks] i) Are demand functions affected...
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two...
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two consumers have the following Cobb-Douglas utility function defined over consumption of goods X and Y: where 0 < β < 1. Each consumer has a different income, consumer 1 has income 1, while consumer 2 has income 12. For now, we will treat the income of each consumer as given. Denote aggregate income as I 12. (a) (10 points) Derive each consumer's individual Marshallian...
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...
1 for good x2 5. Given the market prices p a consumer with U(x1, x2) income $300. Now the price of good x changes. Find the uncompensated and compensated demand for good x 2 for good xı and p2 4x152i maximizing her utility with her
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 + x2. a) Let pı = 2 ,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p1 = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1, p2 = 4 and m = 4. Compared to point b),...
4. General Equilibrium An economy consists of two consumers, indexed by j = A, B, who consume two goods x, and x2. The first consumer's endowment of the two goods is (W1,W4) = (2,4), and the second consumer's endowment is (w,w) = (5,1), where w/ denotes consumer j's endowment of good i. a. Suppose the preferences of the two consumers are described by the utility functions U,(x) = (x^)(x4)4 and U2(x) = xPx, where x denotes consumer j's consumption of...
Consider the following function: where x1 2 0,0,A 0, 0<1. a) Suppose that the preferences of a consumer regarding the consumption of goods x1 and x2 are represented by function = f(x1,x2) above. Suppose also that the consumer is endowed with some disposable income Y > 0 and faces prices pı and p2 respectively for goods x1 and x2. i) Derive and describe the demand of the consumer for goods x1 and x2. [20 marks] i) Are demand functions affected...
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two consumers have the following Cobb-Douglas utility function defined over consumption of goods X and Y: where 0 < β < 1. Each consumer has a different income, consumer 1 has income 1, while consumer 2 has income 12. For now, we will treat the income of each consumer as given. Denote aggregate income as I 12. (a) (10 points) Derive each consumer's individual Marshallian...
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