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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