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:
<u>In the United States</u>
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.
<u>In France</u>
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?
<u>In the United States</u>
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.
<u>In France</u>
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.