Question

Suppose the market for widgets can be described by the following​ equations: ​Demand: P equals 14minus2.00Q ​Supply: P equals 2.00Qminus4​, where P is the price in dollars per unit and Q is the quantity in thousands of units. What is the equilibrium price and​ quantity? The equilibrium quantity is 4.5 thousand units and the equilibrium price is ​$ 5. ​(Enter your responses rounded to two decimal places.​) Suppose the government imposes a tax of ​$1 per unit to reduce widget consumption and raise government revenues. What will be the new equilibrium​ quantity? What price will the buyer​ pay? What amount per unit will the seller​ receive? The new equilibrium quantity will be 4.25 thousand units. ​(Enter your response rounded to two decimal places.​) The price paid by buyers will be ​$ 5.5. ​(Enter your response rounded to two decimal places.​) The amount kept by sellers will be ​$ 4.5. ​(Enter your response rounded to two decimal places.​)

Answer 1

Step-by-step explanation:

Demand P = 14 - 2Q

Supply P = 2Q - 4

Since Demand = Supply

14 - 2Q = 2Q - 4

Collect the like terms on either side

-2Q - 2Q = -4 - 14

-4Q = -18

Dividing both sides by -4, we will have

Q = -18/-4

Q = 4.50 units

P = 14 - 2Q

P = 14 - 2(4.5)

P = 14 - 9

P = $5.00

Therefore Equilibrium price is $5.00 and Equilibrium unit is 4.50

If the government impose a tax of $1 per unit. If price paid but buyer is P, then price received by seller will be (P - 1)

for demand

P = 14 - 2Q

2Q = 14 - P

Q = 7 - 0.5P

For supply

P = 2Q - 4

Q = 2 + 0.5P

Q = 2+ 0.5(P - 1)

Q = 2 + 0.5P - 0.5

Q = 2-0.5 + 0.5P

Q = 1.5 + 0.5P

if Demand = Supply

7 - 0.5P = 1.5 + 0.5P

Collect the like terms on either sides

-0.5P - 0.5P = 1.5 - 7

-1P = -5.5

Dividing both sides by -1, we will have

P = -5.5/-1

P = $5.50

Q = 1.5 + 0.5P

If we substitute 5.5 for P in the above eqn, we will have

Q = 1.5 + 0.5(5.5)

Q = 1.5 + 2.75

Q = 4.25 units