Question

In both the United States and France, the demand for haircuts is given by QD=300−10P . However, in the United States, the supply is given by QS=−300+20P , while in France, the supply is given by QS=−33.33+6.67P .
Required:
a. What are the equilibrium prices and quantities of haircuts in the two countries?
b. What are the new equilibrium prices and quantities of haircuts in the two countries?

Answer 1

Answer:

a. P = 20 and Q = 100 in the United States; and also P = 20 and Q = 100 in France.

b. P = 23.33 and Q = 166.70 in the United States; and P = 26 and Q = 140 in France.

Explanation:

Note: The part b of the requirement is not complete. The entire question is therefore represented with the complete pat b before answering the question as follows:

In both the United States and France, the demand for haircuts is given by QD=300−10P . However, in the United States, the supply is given by QS=−300+20P , while in France, the supply is given by QS=−33.33+6.67P .

Required:

a. What are the equilibrium prices and quantities of haircuts in the two countries?

b. Suppose that the demand for haircuts in both countries increases by 100 units at each price, so that the new demand is QD = 400 - 10P. What are the new equilibrium prices and quantities of haircuts in the two countries?

The explanation to the answers is now provided as follows:

a. What are the equilibrium prices and quantities of haircuts in the two countries?

In economics, an equilibrium occurs at point where the quantities demanded is equal to the quantities supplied.

Let Q denotes equilibrium quantity and P denotes equilibrium price, the equilibrium prices and quantities of haircuts in the two countries can therefore be calculated as follows:

In the United States

QD =300 − 10P

QS= −300 + 20P

Since at equilibrium, QD = QS, we can therefore solve for P by equating the two equations above as follows:

300 - 10P = −300 + 20P

300 + 300 = 20P + 10P

600 = 30P

P = 600 / 30

P = 20

To obtain equilibrium quantity, we substitute P = 20 into any QD and QS since at equilibrium QD = QS. Using QD, we have:

Q = 300 – 10(20)

Q = 300 – 200

Q = 100

Therefore, P = 20 and Q = 100 in the United States.

In France

QD = 300 − 10P

QS= −33.33 + 6.67P

Since at equilibrium, QD = QS, we can therefore solve for P by equating the two equations above as follows:

300 - 10P = −33.33 + 6.67P

300 + 33.33 = 6.67P + 10P

333.33 = 16.67P

P = 333.33 / 16.67

P = 20

To obtain equilibrium quantity, we substitute P = 20 into any QD and QS since at equilibrium QD = QS. Using QD, we have:

Q = 300 – 10(20)

Q = 300 – 200

Q = 100

Therefore, P = 20 and Q = 100 also in France.

b. Suppose that the demand for haircuts in both countries increases by 100 units at each price, so that the new demand is QD = 400 - 10P. What are the new equilibrium prices and quantities of haircuts in the two countries?

In the United States

QD = 400 − 10P

QS= −300 + 20P

Since at equilibrium, QD = QS, we can therefore solve for P by equating the two equations above as follows:

400 - 10P = −300 + 20P

400 + 300 = 20P + 10P

700 = 30P

P = 700 / 30

P = 23.33

To obtain equilibrium quantity, we substitute P = 20 into any QD and QS since at equilibrium QD = QS. Using QD, we have:

Q = 400 – 10(23.33)

Q = 400 – 233.30

Q = 166.70

Therefore, P = 23.33 and Q = 166.70 in the United States.

In France

QD = 400 − 10P

QS= −33.33 + 6.67P

Since at equilibrium, QD = QS, we can therefore solve for P by equating the two equations above as follows:

400 - 10P = −33.33 + 6.67P

400 + 33.33 = 6.67P + 10P

433.33 = 16.67P

P = 433.33 / 16.67

P = 25.99 = 26

To obtain equilibrium quantity, we substitute P = 20 into any QD and QS since at equilibrium QD = QS. Using QD, we have:

Q = 400 – 10(26)

Q = 400 – 260

Q = 140

Therefore, P = 26 and Q = 140 in France.