Question

1. a) The government is contemplating introducing one of two alternative taxes: a tax on commodity x (that would double the price of x, expressed in terms of the numeraire good, y) and a lump sum tax. Assume that the government knows the preferences (i.e., the indifference mapy of a representative taxpayer and his/her indifference curves have the usual convex shape. Suppose that government could predict how much tax revenue it could raise if it introduced the commodity tax. With the aid of a fully labeled graph, show that the government could raise the same tax revenue by means of lump-sum tax on y, where y is a numeraire good, while allowing the representative taxpayer to enjoy a greater utility than he/she would experience with the commodity tax on x. b) Could the government instead impose a lump-sum tax that would leave the taxpayer exactly as well-off as he/she would be with the commodity tax, but would enable the government to raise more tax revenue than with the tax on commodity x? Explain with the aid of a separate fully labeled diagram. 2. Consider a linear demand function in (Q.P) space with vertical intercept (0.a) and horizontal intercept (5,0). Consider an arbitrary point, denoted d, on the demand line. Beginning with the definition of point elasticity of demand, show that it is equal to (bd/ad). 3. Suppose that a monopolist faces a linear demand curve having a vertical intercept of (0,a) and a horizontal intercept of (1,0). Denote the midpoint on the segment ab by the letter 'm' tie., am - bm) and let (Q*.P*) denote the coordinates at point 'm'. A student in ECON 2010 once provided the following argument: "A profit-maximizing monopolist who sells all units at a uniform price will never produce more than Q* (or alternatively, will never charge a price below P) since doing so will lower total revenue, and by producing more, increase total cost. Even if the cost of production were zero, the monopolist's profits would fall if it produced more than Q"." Is the student's argument correct? If so explain clearly why the student's argument is correct. If not explain why the student's argument is wrong.

Answer 1

1. 100 let the price of goodly = E1 (: numeraire) all Price of good a= Pa. Bol (ma money income) .Px + y(i)= m pa ty=m. After quantity tam lie on per unit of commodity at ] Budget line becomes ! _(patt) +4=mi After lump- sum tax of same amount , budget line becomes: para+ 4 m - tai Onty of goody Initial Bl: AB Pivested BL: AB! (anty tax) shifted BL: Alb" (Cump-sum tax ) IC Ī TET T Anty of good ont Biall a B m m -ta') m (Patty par | As shown in the diagram, a & the initiae anty of gooda. when anty tax is imposed , BL piverts from AB to AB' new mes' &d' is the new quity when lump sum is imposed, Bl shifte from AB To A"B" hez Em is established ? quity us purchased because eg is the new equillibrium rather thans er.