The choice of utility function depends on consumer preference which then determines the market behaviour of...
The choice of utility function depends on consumer
preference which then determines the market behaviour of the
market.
Suppose the utility function of a consumer Cobb-Douglas utility
function (CDF)
U(x1, x2) =
x13/5x13/5.
If p1 = p2 = 2 and I =
14
Question 2 - (30
marks)
Calculate and Illustrate the Income
and Substitution Effect when the price of good 1 inctease by
100%
(10 marks)
Calculate the Income Elasticity of
Demand for both goods when the income increase by 100% and
interpret your result.
(10 marks)
Calculate the Price Elasticity of
Demand for both Goods when the price increase by 100% and
interpret your result.
(10 marks)
it is trust me, copy and pasted straight from the source, one of your colleagues asked the same thing before they answered #1.
Homework Answers
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The choice of utility function depends on consumer
preference which then determines the market behaviour of...
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗...
1. When a consumer has a Cobb-Douglas utility function given by u(x, y) = xa yb , their demand for good x is given by x∗ = m/Px (a/a+b) where m is income and Px is the price of good x. Using this demand function, find the formula for this consumer’s price elasticity of demand. Interpret it in words.
X-EC2010-1 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility,...
X-EC2010-1 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(X.y) = x10y10, subject to the constraint that all income, M, is spent on x and/or y. Products x and y are priced at Px and Py, respectively. (a) Set up the appropriate lagrangian for this maximisation problem, find the appropriate first-order conditions for this lagrangian and solve for x and y in terms of px, Py and M. (40 marks) (6) For product...
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y,...
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(x,y) = x1910, subject to the constraint that all income, M, is spent on x and/or y. Products x and y are priced at px and Py, respectively. (a) Set up the appropriate lagrangian for this maximisation problem, find the appropriate first-order conditions for this lagrangian and solve for X and y in terms of Px. Py and M. (40 marks) (b)...
Consumer A has a Cobb -Douglas utility function with exponents that sum to 1. Consumer B...
Consumer A has a Cobb -Douglas utility function with exponents that sum to 1. Consumer B consumes the same two goods, but the goods are perfect substitutes for her. Can Consumer A and Consumer B have the same price offer curves?
Consumer's Surplus A consumer has the utility function U(, y)v) where is the good in concern...
Consumer's Surplus A consumer has the utility function U(, y)v) where is the good in concern ail y is the money that can be spent on all other goods (so the price of y is normalized to be 1). The income of - this consumer is 100. Bi Pr X10 (In(x)y) (10%) Derive the demand function of z for this consumer. (10%) Calculate the price elasticity of the demand function in (b) Is it true that the absolute value of...
Compute the market demand function (as a function of prices and income y) corresponding to a...
Compute the market demand function (as a function of prices and income y) corresponding to a Cobb-Douglas utility function with equal coefficients a1= 1/3 and a2=1/3. What are the demands at prices p1=p2=1 and income y=10? Suppose the price of good 1 rises to 2. Compute the price effects, substitution effects and income effects for the two goods.
A consumer uses his income I for the consumption of two goods ?1 and ?2. He maximises utility at given product prices ?1...
A consumer uses his income I for the consumption of two goods ?1 and ?2. He maximises utility at given product prices ?1, ?2. His preferences with respect to both products can be described by an ordinal utility function ?(?1,?2), which exhibits a decreasing marginal rate of substitution (normal preferences). Please indicate whether the following statements are right or wrong in this context. If a statement is wrong, then describe briefly what is wrong (one sentence). a) A double value...
Question 1 a. In the theory of consumer behaviour, several assumptions are made about the nature...
Question 1 a. In the theory of consumer behaviour, several assumptions are made about the nature of preferences. What are these assumptions? llustrate the significance of these assumptions using indifference curves. b. Discuss why the utility is maximised when the marginal utility per additional dollar spent on one good equals the marginal utility per additional dollar spent on the other good. c. Explain the difference between the income effect and the substitution effect of a price decrease. d. Consider the...
7. A consumer has the following utility function for goods X and Y: U(X,Y) 5XY3 +10...
7. A consumer has the following utility function for goods X and Y: U(X,Y) 5XY3 +10 The consumer faces prices of goods X and Y given by px and py and has an income given by I. (5 marks) Solve for the Demand Equations, X (px,py,I) and Y*(px,py,I) a. b. (5 marks) Calculate the income, own-price and cross-price elasticities of demand for X and Y
Consider a consumer whose utility function is given by U(x, y) = x^1/4y^1/2, where x and...
Consider a consumer whose utility function is given by U(x, y) = x^1/4y^1/2, where x and y represent quantities of consumption of two consumer goods. (a) Derive and interpret the consumer’s Marshallian demand functions for x and y. (b) Derive and interpret the consumer’s Indirect Utility Function. (c) If the consumer’s income is $1000 and the prices of x and y are both $5, how should the consumer maximize her utility? What is her maximum level of utility? (d) Suppose...
X-EC2010-1 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(X.y) = x10y10, subject to the constraint that all income, M, is spent on x and/or y. Products x and y are priced at Px and Py, respectively. (a) Set up the appropriate lagrangian for this maximisation problem, find the appropriate first-order conditions for this lagrangian and solve for x and y in terms of px, Py and M. (40 marks) (6) For product...
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(x,y) = x1910, subject to the constraint that all income, M, is spent on x and/or y. Products x and y are priced at px and Py, respectively. (a) Set up the appropriate lagrangian for this maximisation problem, find the appropriate first-order conditions for this lagrangian and solve for X and y in terms of Px. Py and M. (40 marks) (b)...
Consumer's Surplus A consumer has the utility function U(, y)v) where is the good in concern ail y is the money that can be spent on all other goods (so the price of y is normalized to be 1). The income of - this consumer is 100. Bi Pr X10 (In(x)y) (10%) Derive the demand function of z for this consumer. (10%) Calculate the price elasticity of the demand function in (b) Is it true that the absolute value of...
Question 1 a. In the theory of consumer behaviour, several assumptions are made about the nature of preferences. What are these assumptions? llustrate the significance of these assumptions using indifference curves. b. Discuss why the utility is maximised when the marginal utility per additional dollar spent on one good equals the marginal utility per additional dollar spent on the other good. c. Explain the difference between the income effect and the substitution effect of a price decrease. d. Consider the...
7. A consumer has the following utility function for goods X and Y: U(X,Y) 5XY3 +10 The consumer faces prices of goods X and Y given by px and py and has an income given by I. (5 marks) Solve for the Demand Equations, X (px,py,I) and Y*(px,py,I) a. b. (5 marks) Calculate the income, own-price and cross-price elasticities of demand for X and Y
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