Question

John's T-shirt business uses the demand function P=-Q+ 26 and the supply function P = Q-10. According to these functions, what will the equilibrium point (P, Q) be for John's T-shirt business?

A. (8, 18)
B. (10, 26)
C. (18, 8)
D. (26, 10)

Answer 1

The equilibrium point for John's T-shirt business, which is when quantity demanded equals quantity supplied, is (8, 18), corresponding to option A.

Step-by-step explanation:

To find the equilibrium point for John's T-shirt business, we need to set the demand function equal to the supply function. This is because at equilibrium, the quantity demanded (Qd) is equal to the quantity supplied (Qs). The demand function is given as P = -Q + 26, and the supply function as P = Q - 10. Setting them equal to each other, we get:

-Q + 26 = Q - 10

Adding Q to both sides and adding 10 to both sides gives us:

26 + 10 = Q + Q

36 = 2Q

Dividing both sides by 2, we find Q = 18. Now, we can substitute Q back into either the demand or supply function to find P. Using the supply function:
P = Q - 10 = 18 - 10 = 8

Therefore, the equilibrium point (P, Q) is (8, 18), making the correct answer A. (8, 18).