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 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 &price±on 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 &price±on the demand curve; we need this just to calculate the DWL. The DWL is given by 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 &distortion±(the distance between the equilibrium price and the free market price) is actually a bit hard to de²ne, esp. in the case of taxes and subsidies since two prices really exist. If one de²nes the distortion as the largest of the price distortions (and one de²nes another &price± 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
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& In the short run, MC and AC go up by $1 per unit to 2 and AC 2 : & Simultaneously, short run supply goes up by $1 per unit to S 2 and long run supply also goes up $1 to SL 2 : & P " by < 1 to P 1 ; Q # to Q 1 ; q # to q 1 & Firms make negative pro&t at P 1 ;q 1 ( P 1 < AC 1) , so there will be entry. Long run: & Entry will shift short run supply to the left to S 3 , driving price up to P 2 : & At P 2 ; each &rm will produce q 0 again, but now there will be fewer &rms, so the market quantity will be Q 2 : (b) A technology change reduces &xed costs.
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PS4and5F07s - Economics 101, Problem Set 4 and 5 Solutions....

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