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Assignment 3 – AK 1. QD = 40 - .5P; Qs = 2.5 + 2.5 P a) In equilibrium: QD = QS 40 - .5P = 2.5 + 2.5 P 37.5 = 3P P* = 12.5 Q * = 40 – 12.5/2 = 33.75 ( or 3,375 bil. bushel unit) b) Graph 2. QD = 2000-20P + 5Y; QS = -1000 + 30P a) In equilibrium: QD = QS 2000-20P + 5Y = -1000 + 30P 3000 + 5Y = 50 P P* = Y/10 + 60 When income increases by one dollar, equilibrium price increases by .1 dollar. Q* = -1000 + 30P = -1000 + 30(Y/10 + 60) = 3Y + 800 When income increases by 1 dollar, equilibrium quantity increases by 3. b) Y = 10,000 P* = 10/10 + 60 = 61; Q * = 3*10 + 800 = 830 Y = 40,000 P *= 40/10 + 60 = 64; Q* = 3*40 + 800 = 920 b) Graph 3. QD = 50 – P; QS = 20 + 2P a) In equilibrium: QD = QS 50 – P = 20 + 2P 30 = 3P P* = 10; Q* = 20+2*10 = 40 b) Government imposes the sale tax $T/unit QD = 50 – (P+T) the demand shifts to the right (given the same market price, the consumers now demand less because they have to pay tax). The graph shows that, the equilibrium quantity declines, the market price reduces too due to lower quantity; but the price that consumers have to pay increases due to the tax. c) Equilibrium price and quantity In equilibrium: QD = QS 50 – (P + T) = 20 + 2P 30 – T = 3P P * = 10 – T/3 If T increases by $1, the market price in equilibrium decreases by one-third dollar. P** = P + T = 10 + 2T/3 The price consumers pay in equilibrium increases by two-third dollars if tax increases by $1. Q* = 20+2P = 20 + 2(10-T/3) = 40 – 2T/3 If T increases by $1, the equilibrium quantity decreases by two-third unit. d) T = $3 P** = 10+2*3/3 = 12; Q* = 40-2*3/3 =38 As a result of the tax, consumers have to pay higher price and The price that the producer receives is the market price P* = P** - T = 38 – 3/3 = 37 4. QD = 500 – 5P; QS = 100 + 5P a) QD = QS P* = 40; Q* = 300 b) P = 50 QD = 500 – 5*50 = 250; QS = 100 + 5*5 =350 QD> QS there is a surplus (the price is too high too much supply) the producers will have to adjust by reducing their output supplied which allows them to reduce price. Given that lower price, consumers will in turn increase their quantity demanded. So on and so forth. Finally the market will reach the equilibrium with lower quantity and lower price. The surplus is eliminated. c) Demand shifts down by 20% : QD’ = 500(1-.2) – 5P = 400 – 5P Supply shifts down by 30%: QS’ = 100(1-.3) + 5P = 70 + 5P In equilibrium: QD’ = QS’ 400 – 5P = 70 + 5P P*’ = 33; Q*’ = 235 Compared to before, both the new equilibrium quantity and price decrease. Lower cost allows producers to produce more output at any price level. Without a decline in demand, this cost reduction would result in lower price and higher quantity. However, at the same time, demand reduces, meaning that at every price level, the quantity demanded becomes lower. This effect offsets the effect from the supply side. Eventually we see lower price and lower quantity in equilibrium. d) The industry would be better off not making the investment as measured by a decline in producer surplus, which can be seen clearly from the graph (also intuitively because both price and quantity reduce due to this technology). If you want to verify, calculate the surpluses in two cases: Without technology: PS = (100-40)*300/2 = 9,000 With the technology: PS‘ = (70-33)*235/2 = 4,347.5 < PS