Question

Find the market equilibrium point for the following demand and supply functions.

Demand:        p = -4q + 310

Supply:          p = 6q + 1

p = ?

2nd question:

A shoe store owner will buy 13 pairs of a certain shoe if the price is $73 per pair and 33 pairs if the price is $23. The supplier of the shoes is willing to provide 22 pairs if the price is $76 per pair but only 2 pairs if the price is $24. Assuming the supply and demand functions for the shoes are linear, find the market equilibrium point.

Part 1 of 10

Find the two ordered pairs for the demand function in the form (q, p). List your answers from smallest q to largest.
(q, p) = (? )
(q, p) = ( ? )

Answer 1

Answer :

1) Demand function is p = -4q + 310

Supply function is p = 6q + 1

For the market equilibrium point set -4q + 310 = 6q + 1

10q = 309

q = 30.9

Hence , from demand equation p = -4(30.9) + 310 = 186.4

therefore , p = 186.4

2) Consider the points ( 13, 73) and ( 33, 23)

The slope is m = ( 23-73)/(33-13) = -5/2

The demand equation is

p - 73 = -(5/2)(q - 13)

p = -(5q/2) +(211/2)

Consider the points (22 , 76) and ( 2, 24)

The slope is m= ( 24-76)/(2-22) = 13/5

The supply equation is  

p - 76 =(13/5)(q-22)

p = (13q/5) + (94/5)

For the market equilibrium point set

-(5q/2) +(211/2) = (13q/5) + (94/5)

Multiply by 10 on both sides , we get

-25q + 1055 = 26q + 188

51q = 867

q = 17 and so from demand equation p =63

The market equilibrium point is ( q , p ) = ( 17 , 63)