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Let a consumer have the following utility function.
(a) Sketch some indifference curves of the consumer. Find the marginal rate of substitution (MRS) at any vector of goods x=(x1,x2) and explain the relationship between the indifference curves and the MRS.
(b) Set up the consumer's utility maximization problem and find the demand at any given vector of prices p = (p1,p2)>>0 and income M>0. Are the goods normal or inferior?