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. )

Question

Steve Harrell

Business

9 April, 18:39

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. )

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Answers (1)

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Isiah Sweeney · Answer 1

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