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PS4and5F07s

# PS4and5F07s - Economics 101 Problem Set 4 and 5 Solutions...

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Economics 101, Problem Set 4 and 5 Alan C. Marco Solutions. 25. Suppose demand is given by p = 100 ° 2 Q and supply is given by p = 1 2 Q: Give the equilibria for the following situations: (a) The free market equilibrium 100 ° 2 Q = Q 2 Q ° = 40 P ° = 20 (b) A tax of \$15. 100 ° 2 Q ° 15 = Q 2 Q ° = 34 P s = 17 P d = 32 The DWL is given by DWL b = ° Q ± ° P ± 1 2 = (40 ° 34)(32 ° 17) 1 2 = 45 Note that ° P is just the di/erence between demand and supply along the price axis at the equilibrium quantity. It°s not really a ±change²in price. We just use it to measure the height of the DWL triangle. (c) A subsidy of \$20. 100 ° 2 Q + 20 = Q 2 Q ° = 48 P s = 24 P d = 4 The DWL is given by DWL c = ° Q ± ° P ± 1 2 = (48 ° 40)(24 ° 4) 1 2 = 80 (d) A price °oor at \$40. The price ³oor will be binding, so Q ° will be given by the quanity demanded. 100 ° 2 Q = 40 Q ° = 30 P = 40 P s = 15 1

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P s = 15 is the ±price²on the supply curve; we need this just to calculate the DWL. The DWL is given by DWL d = ° Q ± ° P ± 1 2 = (40 ° 30)(40 ° 15) 1 2 = 125 (e) A price ceiling at \$10. The price ceiling will be binding, so Q ° will be given by the quanity supplied. Q 2 = 10 Q ° = 20 P = 10 P d = 40 P d = 40 is the ±price²on the demand curve; we need this just to calculate the DWL. The DWL is given by DWL e = ° Q ± ° P ± 1 2 = (40 ° 20)(40 ° 10) 1 2 = 300 (f) For (b) through (e), show that the deadweight loss is related to the quantity distortion (at least in rank order). [You must calculate the actual DWL for each case.] Is DWL related to the price distortion? Part DWL Q distortion Price distortion (e) 300 20 20-10=10 (d) 125 10 40-20=20 (c) 80 8 24-20=4 or 20-4=16 (b) 45 6 32-20=12 or 20-17=3 You can see that the quantity distortion is in line with the DWL. Price ±distortion²(the distance between the equilibrium price and the free market price) is actually a bit hard to de´ne, esp. in the case of taxes and subsidies since two prices really exist. If one de´nes the distortion as the largest of the price distortions (and one de´nes another ±price² in the case of price ³oors and ceilings), one can actually get a similar ranking. But, it°s really much easier to do this with quantity, since that°s always observable. 26. Suppose the (perfectly competitive) market for wheat is initially at a short-run and long-run equilibrium. Show (using a two-panel graph of the ±rm and the market) the short-run and long-run impact on p; Q (market quantity), and q (±rm quantity) of the following events: (a) A tax increases per-unit costs by \$1 per unit. P q AC1 MC1 AC2 MC2 q1 q0 P2 P1 P0 P Q D S3 SL2 Q1 Q2 P2 P1 P0 SL1 S2 S1 Q0 Short run: 2