Economics 101, Problem Set 4 and 5Alan C. MarcoSolutions.25.Suppose demand is given byp= 100°2Qand supply is given byp=12Q:Give the equilibria for the followingsituations:(a)The free market equilibrium100°2Q=Q2Q°=40P°=20(b)A tax of $15.100°2Q°15=Q2Q°=34Ps=17Pd=32The DWL is given byDWLb=°Q±°P±12=(40°34)(32°17)12=45Note that°Pis just the di/erence between demand and supply along the price axis at the equilibriumquantity. 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°2Q+ 20=Q2Q°=48Ps=24Pd=4The DWL is given byDWLc=°Q±°P±12=(48°40)(24°4)12=80(d)A price °oor at $40.The price ³oor will be binding, soQ°will be given by the quanity demanded.100°2Q=40Q°=30P=40Ps=151
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Ps= 15is the ±price²on the supply curve; we need this just to calculate the DWL. The DWL is given byDWLd=°Q±°P±12=(40°30)(40°15)12=125(e)A price ceiling at $10.The price ceiling will be binding, soQ°will be given by the quanity supplied.Q2=10Q°=20P=10Pd=40Pd= 40is the ±price²on the demand curve; we need this just to calculate the DWL. The DWL is givenbyDWLe=°Q±°P±12=(40°20)(40°10)12=300(f)For (b) through (e), show that the deadweight loss is related to the quantity distortion (at least in rankorder). [You must calculate the actual DWL for each case.] Is DWL related to the price distortion?PartDWLQ distortionPrice distortion(e)3002020-10=10(d)1251040-20=20(c)80824-20=4 or 20-4=16(b)45632-20=12 or 20-17=3You can see that the quantity distortion is in line with the DWL. Price ±distortion²(the distance betweenthe equilibrium price and the free market price) is actually a bit hard to de´ne, esp. in the case of taxesand 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 similarranking. 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 onp; Q(marketquantity), andq(±rm quantity) of the following events:(a)A tax increases per-unit costs by $1 per unit.PqAC1MC1AC2MC2q1q0P2P1P0PQDS3SL2Q1Q2P2P1P0SL1S2S1Q0Short run:2