At $ 0.49 per bushel, the daily supply for wheat is 409 bushels, and the daily demand is 589 bushels. When the price is raised to $ 0.85 per bushel, the daily supply increases to 529 bushels, and the daily demand decreases to 229 bushels. Assume that the price-supply and price-demand equations are linear.

(A) Find the supply equation.

(B) Find the demand equation.

(C) Find the equilibrium price and quantity

(A) Find the supply equation.

Qs = 245.67 + 333.33Ps

(B) Find the demand equation.

Qd = 1079 - 1000Pd

(C) Find the equilibrium price and quantity

Price P = $0.625

Quantity Q = 454 bushels

Step-by-step explanation:

The demand equation is of the form;

Q = a - bP

The supply equation is of the form;

Q = c + eP

We need to determine the values of a, b, c, d;

At $ 0.49 per bushel, the daily supply for wheat is 409 bushels, and the daily demand is 589 bushels

589 = a - b (0.49) ... 1

409 = c + e (0.49) ... 2

When the price is raised to $ 0.85 per bushel, the daily supply increases to 529 bushels, and the daily demand decreases to 229 bushels;

229 = a - b (0.85) ... 3

529 = c + e (0.85) ... 4

Subtract equation 3 from 1

589-229 = b (0.85) - b (0.49)

360 = b (0.36)

b = 360:0.36

b = 1000

Using equation 1

589 = a - 1000 (0.49)

a = 589+490 = 1079

Subtract equation 2 from 4

529-409 = e (0.85) - e (0.49)

120 = 0.36e

e = 120/0.36

e = 333.33

Using equation 2

409 = c + 333.33 (0.49)

c = 409 - 333.33 (0.49)

c = 245.67

Therefore the demand equation is;

Qd = 1079 - 1000Pd

The supply equation is;

Qs = 245.67 + 333.33Ps

The equilibrium price is at Qs = Qd and Ps = Pd

1079-1000P = 245.67 + 333.33P

P = (1079-245.67) / (1000+333.33)

P = $0.625

Qd = 1079 - 1000 (0.625)

Qs = Qd = 454