1. There are two perfectly divisible goods that can be consumed in non- negative amounts. The consumer's utility function is new) = M+ E (a) Sketch a typical indifference curve. If prices and income are strictly positive (and nite), is there always an interior solution to the con- sumer's problem, i.e., does the consumer always demand positive amounts of both commodities? (b) Derive the demand function for commodity 1. (c) Let m'\" 2 (mix? be the demands for the two goods when m = 24 and p1 2 p2 = 1. Calculate 517*. (d) Suppose the government imposes a tax of $1 per unit on commodity 1, so the consumer faces prices (2, 1) and m remains 24. What are the new demands? How much tax revenue does the government collect? What is the consumer's utility? (e) Suppose that instead of a commodity tax the government imposes a lump-sum tax, reducing the consumers income from 24 to m' while prices remain (1, 1). What is the value of m' such that when the con- sumer maximizes utility with prices (1,1) and income m' she receives the same utility as in (d)? How much tax revenue does the government collect through such a lump-sum tax? (f) Compare the two tax schemes from the point of view of the consumer and the government. (Does the consumer/ government prefer one tax scheme over the other?)