Functions of two or more independent variables a. An individual's utility function has the Cobb-Douglas form: U=X0.5y2 where U is an index of her utility and X and Y are the weekly quantities of the two goods consumed. Find the marginal utilities of the two goods. Does the consumer ever experience satiation with respect to either good? b. How does the marginal utility of each good vary as consumption of it increases with consumption of the other good held constant? What is the economic significance of the signs of these partial derivatives? c. By differentiation, show that the indifference curve is negatively sloped and convex in the KL plane. Give an economic interpretation to the slope and curvature of the indifference curve. Sketch the graph of the indifference curve.
Functions of two or more independent variables a. An individual's utility function has the Cobb-Douglas form: U=X0.5y2 where U is an index of her utility and X and Y are the weekly quantities of the two goods consumed. Find the marginal utilities of the two goods. Does the consumer ever experience satiation with respect to either good? b. How does the marginal utility of each good vary as consumption of it increases with consumption of the other good held constant? What is the economic significance of the signs of these partial derivatives? c. By differentiation, show that the indifference curve is negatively sloped and convex in the KL plane. Give an economic interpretation to the slope and curvature of the indifference curve. Sketch the graph of the indifference curve.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.11P
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Elements of Mathematical Economics
Transcribed Image Text:P4: Functions of two or more independent variables
X0.5y2 where U
a. An individual's utility function has the Cobb-Douglas form:
is an index of her utility and X and Y are the weekly quantities of the two goods
consumed. Find the marginal utilities of the two goods. Does the consumer ever
experience satiation with respect to either good?
b. How does the marginal utility of each good vary as consumption of it increases
with consumption of the other good held constant? What is the economic
significance of the signs of these partial derivatives?
c. By differentiation, show that the indifference curve is negatively sloped and
convex in the KL plane. Give an economic interpretation to the slope and
curvature of the indifference curve. Sketch the graph of the indifference curve.
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