Homework Answers
3. A. Yes, because the partial derivative with respect to m is
positive.
(A good is normal when its demand increases with increase in
income. So, 
whiche means as m increases by 1 unit, x2 will increase by 2/3p2
units. So, it is a normal good.)
4. unrelated
(As the demand for good 2 is not dependent on the price of good 1
so they are unrelated.)
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Question 3 5 pts with respective Suppose the consumer is in a two good world, and...
A consumer has the following preferences u(11, 12) = log (11) + 12 Suppose the price...
A consumer has the following preferences u(11, 12) = log (11) + 12 Suppose the price of good 1 is pı and the price of good 2 is P2. The consumer has income m. (a) Find the optimal choices for the utility maximization problem in terms of P1, P2 and m. Denote the Lagrange multiplier by 1. (b) How do the optimal choices change as m increases? What does the income offer curve (also called the income expansion path) look...
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...
Problem 2 (30 marks) A consumer has a utility function (11,12)= = = (a) Express the...
Problem 2 (30 marks) A consumer has a utility function (11,12)= = = (a) Express the consumer's demand for good l as a function of prices and income. (b) Draw an Engel curve for the consumer's demand for good 1 when the prices are given by Pi = 1, and P2 = 1. (c) Draw another Engel curve for the consumer's demand for good 1 when the prices are given by Pi = 1, and p2 = 3. (d) Draw...
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...
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....
A basket of goods for a given consumer includes two goods, X and Z. Consumer income...
A basket of goods for a given consumer includes two goods, X and Z. Consumer income is equal to $1,000 and the prices of these two goods are as follows: Px = $20 P2 = $50 This consumer is consuming 10 units of good X. Suppose that over the course of a year, the price of good X changes by - 10% and the price of good Z changes by 10%. How much income would be required for the consumer...
5. Suppose we have the following information on the demand for a good x, for two...
5. Suppose we have the following information on the demand for a good x, for two individuals Alpha and Beta at different prices for good 2 Alpha Beta P2 P2 1.50 1.00 1.00 1.50 Determine the cross price elasticity of demand for Alpha in this case. Determine the cross price elasiticity of demand for Beta in this case. (iv) Comment on the differences in the relationship between changes in the price of good 2 and the quantity demanded of xy...
4. In a two-good world, suppose a consumer views the goods as perfect substitutes. Draw a...
4. In a two-good world, suppose a consumer views the goods as perfect substitutes. Draw a graph of the consumer's choice problem, with a budget constraint and a few indifference curves. (Assume the slope of the indifference curves is different from the slope of the budget constraint.) What is notable about the consumer's preferred bundle?
4. In a two-good world, suppose a consumer views the goods as perfect substitutes. Draw a graph of the consumer's choice problem, with a budget...
7. Suppose you know that a demand function of consumer for good 1 is p-, where...
7. Suppose you know that a demand function of consumer for good 1 is p-, where pi is price of the good and xi is the quantity consumed. You know that the consumer can buy only good 1 or good 2. Her income is $2000 and the price of good 2 is P2 〉 0. (a) Find an utility function that represents the preferences of this consumer (b) Given the above utility function derive demand for good 2. (c) Suppose...
5. Suppose that each consumer has the Cobb-Douglas utility function u:(X1i, X2i) X11 X21-4. In addition...
5. Suppose that each consumer has the Cobb-Douglas utility function u:(X1i, X2i) X11 X21-4. In addition the endowments are wi=(1,2) and w2=(2,1). What should be the vector of prices (pı", p2') in order to achieve equilibrium (supply-demand). [Note use an increasing transformation of the utility functions given by a In Xii+(1-a) In X2i] . . following utility functions:
A consumer has the following preferences u(11, 12) = log (11) + 12 Suppose the price of good 1 is pı and the price of good 2 is P2. The consumer has income m. (a) Find the optimal choices for the utility maximization problem in terms of P1, P2 and m. Denote the Lagrange multiplier by 1. (b) How do the optimal choices change as m increases? What does the income offer curve (also called the income expansion path) look...
Problem 2 (30 marks) A consumer has a utility function (11,12)= = = (a) Express the consumer's demand for good l as a function of prices and income. (b) Draw an Engel curve for the consumer's demand for good 1 when the prices are given by Pi = 1, and P2 = 1. (c) Draw another Engel curve for the consumer's demand for good 1 when the prices are given by Pi = 1, and p2 = 3. (d) Draw...
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...
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....
A basket of goods for a given consumer includes two goods, X and Z. Consumer income is equal to $1,000 and the prices of these two goods are as follows: Px = $20 P2 = $50 This consumer is consuming 10 units of good X. Suppose that over the course of a year, the price of good X changes by - 10% and the price of good Z changes by 10%. How much income would be required for the consumer...
5. Suppose we have the following information on the demand for a good x, for two individuals Alpha and Beta at different prices for good 2 Alpha Beta P2 P2 1.50 1.00 1.00 1.50 Determine the cross price elasticity of demand for Alpha in this case. Determine the cross price elasiticity of demand for Beta in this case. (iv) Comment on the differences in the relationship between changes in the price of good 2 and the quantity demanded of xy...
4. In a two-good world, suppose a consumer views the goods as perfect substitutes. Draw a graph of the consumer's choice problem, with a budget constraint and a few indifference curves. (Assume the slope of the indifference curves is different from the slope of the budget constraint.) What is notable about the consumer's preferred bundle?
4. In a two-good world, suppose a consumer views the goods as perfect substitutes. Draw a graph of the consumer's choice problem, with a budget...
7. Suppose you know that a demand function of consumer for good 1 is p-, where pi is price of the good and xi is the quantity consumed. You know that the consumer can buy only good 1 or good 2. Her income is $2000 and the price of good 2 is P2 〉 0. (a) Find an utility function that represents the preferences of this consumer (b) Given the above utility function derive demand for good 2. (c) Suppose...
5. Suppose that each consumer has the Cobb-Douglas utility function u:(X1i, X2i) X11 X21-4. In addition the endowments are wi=(1,2) and w2=(2,1). What should be the vector of prices (pı", p2') in order to achieve equilibrium (supply-demand). [Note use an increasing transformation of the utility functions given by a In Xii+(1-a) In X2i] . . following utility functions:
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