3.1 Question 39

[Eigenvalue]

Precalculus
Michael Sullivan
Edition 4
Chapter 3, Section 3.1

Suppose that the quantity supplied S and quantity demanded D of T-shirts at a concert are given by the following function

S(p)=-200+50P
D(p)=1000-25p

where p is the price of a t-shirt

a) Find the equilibrium price for t-shirts at this concert. What is the equilibrium quantity?

b) Determine the prices for which quantity demanded is greater than quantity supplied

c) What do you think will eventually happen to the price of T-shirts if quantity demanded is greater than quantity supplied?

[nycmath]

Part A

Set S(p) = D(p)

-200 + 50p = 1000 - 25p

-200 - 1000 = -25p - 50p

-1200 = -75p

-1200/-75 = p

16 = p

The equilibrium price for T-shirts is $16.

[nycmath]

Part B

Set S(p) > D(p)

-200 + 50p > 1000 - 25p

-200 - 1000 > -25p - 50p

-1200 > -75p

-1200/-75 < p

16 < p

T-shirts less than $16 will yield quantity demanded over quantity supplied.

[nycmath]

Part C

If quantity demanded is greater than quantity supplied, a shortage of T-shirts will happen; buyers will compete for the limited number of T-shirts available.

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