Question

Suppose that the demand for textbooks, QD, is represented by the following equation, where P is the price of a textbook and QD is the number of textbooks demanded:

QD =4,000.00−20.00P
The supply of textbooks, Qs, is represented by the equation:
QS=−100.00+10.00P
The equilibrium price is $____ (round your answer to two decimal places).
The equilibrium quantity is____ (round your answer to two decimal places - for the purposes of this problem, imagine it is possible to sell a fraction of a book).

Answer 1

To calculate the equilibrium price and quantity for textbooks, we set the demand equation equal to the supply equation and solve for P. However, it seems there is an error in the equations provided, as they yield a negative demand.

Step-by-step explanation:

To find the equilibrium price and quantity in the market for textbooks, we set the demand equation, QD = 4,000.00 - 20.00P, equal to the supply equation, QS = -100.00 + 10.00P.

By setting QD equal to QS we get:

1. 4,000.00 - 20.00P = -100.00 + 10.00P
2. Adding 20.00P to both sides yields: 4,000.00 = 10.00P + 100
3. Subtracting 100 from both sides: 3,900.00 = 10.00P
4. And dividing both sides by 10.00 we find the equilibrium price: P = 390.00

To find the equilibrium quantity, substitute the value of P back into either the demand or supply equation:

• QD = 4,000 - 20.00(390) = 4,000 - 7,800 = -3,800 (which is not possible in real terms)
• QS = -100 + 10.00(390) = -100 + 3,900 = 3,800

However, since a negative demand makes no sense, it suggests that there may be a mistake in the student's initial equations or in the process of finding the equilibrium.