Suppose demand and supply are given by
2 answers:
Answer:
a. price is $60, quantity is 14.
b. price is $36; quantity is 8
c. $96
Explanation:
A) Equilibrium is when demand is equal to supply
Demand: QXd = 14 - (1/2)PX must be equal to Supply: QXs = (1/4)PX – 1
14 - (1/2)PX = (1/4)PX – 1
- (1/2)PX – (1/4)PX = 1-14
- (1/4)PX = -15
Dividing both sides of the equation with - 1/4, we get
PX = 60.
Price at equilibrium is 60.
Substituting PX=60, into the Supply equation to get the Quantity at equilibrium:
QXs = (1/4)PX – 1
QXs = (1/4)(60) – 1
= 15 – 1
= 14
Quantity at equilibrium is 14.
(please see attachment for graph) EQUILIBRIUM A
B) A $12 excise tax will result in a decrease in demand and supply will remain the same.
QXd = 14 - (1/2)PX + 12
=26 – (1/2)PX
The new equilibrium price and quantity will therefore be:
26 - (1/2) PX = (1/4)PX – 1
(-1/2 -1/4) PX = -26 – 1
-3/4 PX = -27
Dividing both sides by -3/4, we get:
PX = 36
Substituting the new equilibrium price, into the supply equation
(1/4)PX – 1
1/4) (36) – 1 = 8
New equilibrium quantity is 8.
(Please see attached for graph) (EQUILIBRIUM B)
C) Since an excise tax is collected on each unit sold, the amount of revenue received by the government is the amount of the tax multiplied by the quantity sold. Revenue earned by the government from a $12 tax is $12 * 8 = $96.
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C. cyclical unemployment rate is 4 percent.
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