Suppose bundle A is better than bundle B for a consumer, and bundle C is an average of bundles A and B.
a. Use the continuity, convexity and monotonicity assumptions to formally prove that this implies that bundle C is better than bundle B.
b.Did you also -- implicitly or explicitly -- use the rationality axioms?
What will be an ideal response?
that is just as good (but no better) than B, i.e. .
.Next, take the average bundle between
and B -- and call it 
. Convexity implies that 
. is at least as good as B.Finally, note that C contains more of every good than
. Thus, monotonicity implies that C
--- and, since 
is at least as good as B, this implies that C
B.b. Yes, both the completeness and the transitivity assumptions were used. Completeness was used implicitly because we created bundles and just assumed that the consumer is able to compare them to other bundles. Transitivity was used in the last step where we concluded that we know C is better than B because we C is better than
and 
is at least as good as B.You might also like to view...
The payoff matrix of economic profits above displays the possible outcomes for Bob and Jane who are involved in game of whether or not to advertise. After each player chooses his or her best strategy and sees the result
A) only Bob would like to change his decision. B) neither player would be willing to change his or her decision unless the other player also changes his or her decision. C) if Jane does not change her decision, Bob would like to change his. D) if Bob does not change his decision, Jane would like to change hers.
After getting a raise at work, Jasper now regularly buys steak instead of chicken. Which factor of demand has influenced Jasper's demand for steak?
A. Price of a substitute good B. Price of a complementary good C. Income D. Preferences
Which of the following statements is true?
A) An excess supply of credit exerts an upward pressure on the real rate of interest. B) An excess demand for credit exerts an upward pressure on the real rate of interest. C) At rates of interest below the equilibrium rate, there is an excess supply of credit. D) At rates of interest above the equilibrium rate, there is an excess demand for credit.
If a German firm owns a U.S.-based firm that is domiciled in the U.S., the combined firm is subject to the corporate tax laws in ________ and income tax laws in ________.
A) Germany; Germany B) Germany; U.S. C) U.S.; Germany D) U.S.; U.S.