Answer:
(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
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