Question

Suppose that the supply function for honey is p=​S(q)=0.4q+2.8​, 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 ​$4.80 and the demand is 4 barrels when the price is ​$6.90. Find an equation for the demand​ function, assuming it is linear.

Answer 1

Answer:

The demand function is p= (-2.1)*q + 15.3

Explanation:

The supply function for honey is p=​S(q)=0.4*q+2.8​, where p is the price in dollars for an 8​-oz container and q is the quantity in barrels. The equilibrium price is ​$4.80. So, the equilibrium quantity is:

4.80=0.4*q+2.8​

Solving:

4.80 - 2.8=0.4*q

2=0.4*q

2÷0.4= q

5=q

The demand​ function, assuming it is linear, is p=​m*q+b

The equilibrium quantity is 5 barrels and the equilibrium price is ​$4.80; and the demand is 4 barrels when the price is ​$6.90. So:

$\left \{ {{4.80=m*5+b} \atop {6.90=m*4+b}} \right.$

Isolating the variable "b" from the first equation, you get:

4.80 - m*5= b

Replacing the previous expression in the second equation you get:

6.90=m*4 + 4.80 - m*5

6.90 - 4.80=m*4 - m*5

2.1= (-1)*m

2.1÷(-1)= m

-2.1=m

Replacing the value of "m" in the expression 4.80 - m*5= b you get:

4.80 - (-2.1)*5= b

Solving you get:

15.3= b

So, the demand function is p= (-2.1)*q + 15.3