7. Explain what are the Roy’s identity, the Shephard’s lemma and the indirect utility function.
7. Explain what are the Roy’s identity, the Shephard’s lemma and the indirect utility function.
Homework Answers
Shephards lemma - Ronald shephard was the one to provide this theory. The theory states that the consumer have a unique ideal point at which he may buy the product. This defines a relationship between indifference curve and the expenditure of the consumer on that product. We know that utility provided is similar on every point of indifference curve, but the consumer have a fixed point at which the utility function is derived.
Roys identity - Rene Roy provided the theory of Roy's identity. This theory states the relation between demand function and utitlity function. This minimises the cost of the product related to the demand for the product.
Indirect utility function - It provides the maximum number of utility which a consumer can attain taking care of the market prices and the income of the consumer. It reflects both consumer prefrence and competition in the market.
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7. Explain what are the Roy’s identity, the Shephard’s lemma and the indirect utility function.
2) Assume that utility is given by Utility-U(X,Y)-X03yo7 a) Calculate the ordinary demand functions, indirect utility function, and expenditure function. b) Use the expenditure function calculate...
2) Assume that utility is given by Utility-U(X,Y)-X03yo7 a) Calculate the ordinary demand functions, indirect utility function, and expenditure function. b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good X. Use the results from part (b) together with the ordinary demand function for good X to show that the Slutsky equation holds for this case. c) d) Prove that the expenditure function calculated in part (a) is homogeneous...
Derive indirect utility function when facing Px, Py and I; from the below (direct) utility from...
Derive indirect utility function when facing Px, Py and I; from the below (direct) utility from consumption of x and y: U(x,y)=x^0.5+y^0.5 Why do we bother calculating the indirect utility function? Briefly explain.
how to find indirect utility function here? Jeanette has the following utility function: U-ain(x) + b*In(y), where...
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)
5. Consider the indirect utility function given by: m v(P1, P2, m) = P1 + P2 (a) What are the demand functions (b) What...
5. Consider the indirect utility function given by: m v(P1, P2, m) = P1 + P2 (a) What are the demand functions (b) What is the expenditure function? (c) What is the direct utility function?
If so, ind it. I no, explain. 7. Suppose, as usual, Elmos utility function over gambles...
If so, ind it. I no, explain. 7. Suppose, as usual, Elmos utility function over gambles satisfies the expected utility property. Consider two gambles g and h such that E[g]> E[h]. (a) Suppose Elmo is risk-averse. Will Elmo necessarily prefer g to h? Explain. (b) What if Elmo is risk-neutral? Explain. (c) What if Elmo is risk-loving? Explain. QA
7. State (and explain) whether these are monotonic transformations or not for the utility function u...
7. State (and explain) whether these are monotonic transformations or not for the utility function u = (x,y). f(u) = 3.14u f(u) = 5000-23u f(u) = 1/u2
Derive the Marshallian demand functions for Goods X, and X, by maximizing following utility-maximizing problem. What...
Derive the Marshallian demand functions for Goods X, and X, by maximizing following utility-maximizing problem. What restrictions does a Cobb-Douglas lity function (preferences) impose on demand functions? Explain your answer. marks) 1/4 Maximize u = x;"/4x2 4x, + 2x, = 100 Subject to - Use the information in above to derive the consumer's indirect utility anction (value function) and then prove Roy's identity (10 marks)
U=x^2y^2+xy Derive the Marshallian demands and indirect utility function
U=x^2y^2+xy Derive the Marshallian demands and indirect 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. 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....
2) Assume that utility is given by Utility-U(X,Y)-X03yo7 a) Calculate the ordinary demand functions, indirect utility function, and expenditure function. b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good X. Use the results from part (b) together with the ordinary demand function for good X to show that the Slutsky equation holds for this case. c) d) Prove that the expenditure function calculated in part (a) is homogeneous...
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)
5. Consider the indirect utility function given by: m v(P1, P2, m) = P1 + P2 (a) What are the demand functions (b) What is the expenditure function? (c) What is the direct utility function?
If so, ind it. I no, explain. 7. Suppose, as usual, Elmos utility function over gambles satisfies the expected utility property. Consider two gambles g and h such that E[g]> E[h]. (a) Suppose Elmo is risk-averse. Will Elmo necessarily prefer g to h? Explain. (b) What if Elmo is risk-neutral? Explain. (c) What if Elmo is risk-loving? Explain. QA
Derive the Marshallian demand functions for Goods X, and X, by maximizing following utility-maximizing problem. What restrictions does a Cobb-Douglas lity function (preferences) impose on demand functions? Explain your answer. marks) 1/4 Maximize u = x;"/4x2 4x, + 2x, = 100 Subject to - Use the information in above to derive the consumer's indirect utility anction (value function) and then prove Roy's identity (10 marks)
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....
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