Suppose that the supply function for honey is p​=S(q)=0.2q​+22, where p is the price in dollars for

Carole Juarez

Carole Juarez

Answered question

2022-02-24

Suppose that the supply function for honey is p​=S(q)=0.2q​+22, where p is the price in dollars for an ​8-oz container and q is the quantity in barrels. Suppose also that the equilibrium price is ​$4.40 and the demand is 3 barrels when the price is ​$5.80. Find an equation for the demand​ function, assuming it is linear.

Answer & Explanation

mtakadamu9i5

mtakadamu9i5

Beginner2022-02-25Added 8 answers

The honey supply function is
p​=S(q)=0.2q​+2.2 
Where, 
p is the cost for an 8-oz container in dollars, and q is the amount in barrels.
$4.40 is the equilibrium price.
When the price is $5.80, there is a demand for three barrels. Suppose the demand function has the following form: p=D(q)=aq+b
The supply function is provided as p =S(q)=0.2q +2.2.
$4.40 is the specified equilibrium price. The equilibrium quantity is hence
0.2q​+2.2=4.40 
0.2q=4.40-2.2 
0.2q=2.2 
q=2.2/0.2 
q=11 
When we enter q=11 into the demand function, the result is 4.40=11a+b. (1) If the price is $5.80 and the demand is three barrels, then $5.80=3a+b. (2) The system of linear equations is made up of equations (1) and (2).
Add equation (2) less than (1),
4.40 = 11a + b 
-5.80 = 3a + b 
-1.40 = 7a 
a = -1.40/7 
a = -0.2 
Put a=-0.2 in equation (1) 
4.40 = 11(-0.2) + b 
b=4.40-11(-0.2) 
b=6.6 
The demand function is therefore p=D(q)=-0.2q+6.6.

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