Question

At a price of ​$2.25 per​ bushel, the supply of a certain grain is 7400 million bushels and the demand is 7700 million bushels. At a price of ​$2.3 per​ bushel, the supply is 7800 million bushels and the demand is 7600 million bushels. ​(A) Find a​ price-supply equation of the form p=mx+s​b, where p is the price in dollars and x is the supply in millions of bushels.

​(B) Find a​ price-demand equation of the form p=mx+​b, where p is the price in dollars and x is the demand in millions of bushels. ​

(C) Find the equilibrium point.

(D) Graph the​ price-supply equation,​ price-demand equation, and equilibrium point in the same coordinate system.

Answer 1

At a price of ​$2.25 per​ bushel, the supply of a certain grain is 7400 million bushels and the demand is 7700 million bushels. At a price of ​$2.3 per​ bushel, the supply is 7800 million bushels and the demand is 7600 million bushels.

​(A) To find a​ price-supply equation of the form p=mx+s​b, where p is the price in dollars and x is the supply in millions of bushels, we have two equations from the given data;

2.25 = 7400m + sb

2.3 = 7800m + sb

On solving we have ,

2.25 - 7400m = 2.3 -7800m

m = 0.000125

Plugging this m in first equation, we get sb = 1.325

Thus, the required equation is,

p = 0.000125x + 1.325

​(B) To find a​ price-demand equation of the form p=mx+​b, where p is the price in dollars and x is the demand in millions of bushels, we have two equations from the given data,

2.25 = 7700m + sb

2.3 = 7600m + sb

On solving we have,

2.25-7700m= 2.3-7600m

m = -0.0005

Also,

sb = 6.1

Therefore the required equation is,

p = -0.0005x + 6.1

(C) To find the equilibrium point, equating both the equations;

-0.0005x + 6.1 = 0.000125x + 1.325

0.000625x = 4.775

x = 7640

Plugging this value back in supply equation,

p = 2.28

The equilibrium point is ( 7640,2.28)