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Q6 Deriving Demand Function Derive demand functions x1(P1, P2, m) and x2(P1, P2, m) for the...
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2,...
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2, B) and x (P1, P2, B), and calculate 11 (income elasticity of good 1), €1 (own-price elasticity of good 1), and €12 (cross-price elasticity). a U(x1, x2) = 21 b U(x1, x2) = 2.925-a for a € (0,1) CU(21, 12) = ln(21) + x2 where B > P2.
Suppose an individual’s utility function is u=x11/2, x21/2. Let p1=4, p2=5, and income equal $200. With...
Suppose an individual’s utility function is u=x11/2, x21/2. Let p1=4, p2=5, and income equal $200. With a general equation and general prices, derive the equal marginal principle. Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility. What is the optimal amount of x1 consumed? What is the optimal amount of x2 consumed? What is the marginal rate of substitution at the optimal amounts of x1 and x2? As functions of p1, p2, and...
An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3....
An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3. The price of good x1 is p1, the price of good x2 is p2 = 1 and the price of good x3 is p3. The individual’s income is I. Derive the Marshallian demand functions (x1* , x2*, x3* ).
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...
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...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the consumption bundles that gives the consumer utility 100. (3 points) b) Plot all the consumption bundles that gives the consumer utility 144. (3 points) c) Plot the budget constraint when p. = 10,P2 = 10 and m = 100 (3 points) d) Plot the budget constraint when P1 = 20, P2 = 5 and m = 60 (3 points) e) What is the optimal...
6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint...
6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint px + p2x2 = m. Derive the consumer's demand functions for x1 and x2. (25 marks)
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 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...
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2, B) and x (P1, P2, B), and calculate 11 (income elasticity of good 1), €1 (own-price elasticity of good 1), and €12 (cross-price elasticity). a U(x1, x2) = 21 b U(x1, x2) = 2.925-a for a € (0,1) CU(21, 12) = ln(21) + x2 where B > P2.
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...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the consumption bundles that gives the consumer utility 100. (3 points) b) Plot all the consumption bundles that gives the consumer utility 144. (3 points) c) Plot the budget constraint when p. = 10,P2 = 10 and m = 100 (3 points) d) Plot the budget constraint when P1 = 20, P2 = 5 and m = 60 (3 points) e) What is the optimal...
6. Consider a consumer with the utility function u(x1,x2) = In(x) x2 and the budget constraint px + p2x2 = m. Derive the consumer's demand functions for x1 and x2. (25 marks)
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...
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