help here plz

Assume that your grandmother pays for your studies. You probably agree that this assumption is more realistic than most assumptions we make in economics given the cost of living and our "generous" financial support at UC Davis. Imagine the following story: You pay a visit to your grandmother to thank her for her truly generous support. She asks what path-breaking insights you have learned in 200A. After mentioning that the central topic of 200A is consumer theory you proudly tell her that you learned that when prices go up then demand may go up or down. She looks at you with some consternation and starts to wonder whether supporting your studies makes any sense. After all, she knew this all along without having studied 200A. Since you rely on her support, her doubts naturally alarm you. You desperately try to search your memory for something less trivial to tell her. You vaguely recall the "compensated law of demand": For any (p, w), (p', w) with w' =pz(p, w) we have (pp) (r(p,w')-I(p, w)) ?0 (With this notation, pR is a price vector, where L is the number of commodities in the economy; w R. denotes the consumer's wealth; r(p, u) denotes Walrasian demand at prices p and wealth w. Throughout, we assume that r(p, w) is single-valued in R for any p and w.) a.) In order to discuss the "compensated law of demand" with your grandmother, you need a verbal interpretation of it. Give a verbal interpretation of the "compensated law of demand". b.) Your grandmother asks in what sense the "compensated law of demand" is a law. You recall the following proposition that we proved in class: Proposition: Suppose that the Walrasian demand function r(p, w) is homogeneous of degree zero and satisfies Walras' law. Then r(p, w) satisfies the weak ax

2. Consider now the non-trivial case (?) 1(p, w). Rewrite (-p)-(=(, ) - (p?)) = p. (1(P?)-(p,w))-p-(x(P, w')-1(p,w)). Consider separately each term of the right-hand side. Derive the signs of each of the two terms using (some) assumptions of the proposition and the fact that we assumed '-p-rp.) for the compensated law of demand. To derive the sign of the second term of the right-hand side you will need to make use of the weak axiom of revealed preference. 3. Put everything together to conclude the proof of the first direction. c.) Given the characterization of the compensated law of demand by the weak axiom of revealed preference, you need to explain to your grandmother the meaning of the weak axiom of revealed preference. Provide a verbal interpretation of the weak axiom of revealed preference. d.) The weak axiom of revealed preference may be viewed as a condition on the "consistency of consumer choice. We may be inclined to label a consumer violating this condition as being irrational (unless a more complex setting is considered). So the above proposition characterizes the compensated law of demand in terms of consistency of consumer choice. But is it really a characterization in terms of rational consumer choice in the sense of having complete and transitive preferences over consumption bundles? That is, is the following conjecture true? Conjecture: Suppose that the Walranian demand function r(p, w) is homogeneous of degree zero and satufes Walras law. Then zip, w) satisfies the compensated law of demand if and only if the consumer has complete and transitive preferences over consumption bundles Consider both directions of the conjecture separately. Moreover, consider the special case of L2 separately. [You don't have to present a detailed proof You can make use of results learned in class. The line of arguments should be clear)

. Explain the role economics plays in the tradeoffs people and organizations make. Identify the relationship of trade, including comparative and absolute advantage, to the decisions made by domestic firms. . Describe the importance of market forces as they determine market demand and supply versus individual demand and supply. Describe the role elasticity plays in determining demand and pricing dedsions of the firm. . Identify the differences between producer surplus and consumer surplus. . Explain the role taxation plays in supply and demand. . Define marginal utility, total utility, and diminishing utility. . Identify the differences between private, common, and public goods. . Describe the relationship between productivity and the different costs of production, . Describe the various market structures, their characteristics, and the effects of each structure in relationship to the market . Identify the differences between economic and accounting profit. . Explain discrimination in the labor market.Describe income inequality and poverty and the policies to reduce them. . Define the theory of consumer choice and how consumers act to optimize their choices. . Describe ideas in political economy and their use in social choice.1) Under fixed exchange rate, which one of the following statements is the most accurate? A) Devaluation causes a decrease in output. a decrease in official reserves, and a contraction of the money supply. B) Devaluation causes a rise in output, a rise in official reserves, and an expansion of the money supply. C) Devaluation causes a rise in output and a rise in official reserves. D) Devaluation causes a rise in output and an expansion of the money supply. E) Devaluation causes a rise in official reserves and an expansion of the money supply. 2)Under fixed exchange rate, which one of the following statements is the most accurate? A) Devaluation causes a rise in output. B) Devaluation causes a decrease in output. C) Devaluation has no effect on output. D) Devaluation causes a rise in output and a decrease in official reserves. E) Devaluation causes a decrease in output and in official reserves. 3)At negative nominal interest rates, which one of the following statements is the most accurate? A) People would find money strictly preferable to bonds, B) People would find money strictly preferable to bonds and bonds therefore would be in excess supply. (People would find money strictly preferable to bonds and bonds therefore would be in excess demand. Dj People would find money strictly preferable to bonds and the bonds market would be in equilibrium.