Suppose that the supply function for walnuts is pSq025q36 wh

Suppose that the supply function for walnuts is p=S(q)=0.25q+3.6, where p is the price in dollars per pound and q is the quantity in bushels. Suppose also that the equilibrium price is $5.85, and the demand is 4 bushels when the price is $7.60. Find an equation for the demand function assuming it is linear. Use the equation editor and show your work. Hint: There are three steps in this problem. Think about what you need to know in order to find the equation of a line.

Solution

p =0.25q+3.6

Let the demand equation be d = a*q +c

equlibrium price $ 5.85 : 5.85 = 0.25q +3.6

q = 9 bushels

( 9 , $5.85)

where d is the price and q is the quantity

( 4 , $ 7.60)

So, 7.60 = 4a +c ----(1)

Now plug ( 9,$ 5.85) to solve for a and c

5.85 = 9a +c -----(2)

solve equation 1 and 2:

we get a = -0.35 ; c = 9

Plug values of a and c to get demand equation

Demand equation : -0.35q +9