Consider a consumer whose consumption set if given by X = Rf, whose Walrasian demand function satisfies homogeneity of degree zero, Walras' law, and the weak axiom of revealed preference (WARP). Suppose that this consumer's only source of income is her pension income which is equal to w0 > 0 and suppose that the consumer initially faced prices given by the vector p' >> 0. However, due to inflation, prices have increased by 10% and the new price vector that the consumer faces is given by p\" >> 0. The ination rate is calculated as f0||0W33 (Zipffxif' We) Zipfxi (19': W0))/Zipxi(p,:wo) where XEQC'I: W0) is the consumer's Walrasian demand for commodity i. In response to the surge in ination, the government is planning to increase the consumer's pension income by 10%. While answering the following questions, you can assume that the consumer spends all of her pension income, i.e., Z,p,'x,(p',wo) = Wu, and that the consumer's Walrasian demand is single-valued. (a) Suppose that the government increases the consumer's pension income by 10% as proposed. Is the consumer better off or worse off compared to when she faced the price vector p' >> 0 and had income equal to w0 > 0? Please explain your reasoning and state all the assumptions that you made while reaching your conclusion. (b) Is the government's proposed plan sensible? Can you think of any alternatives to this plan