Question

The equilibrium price for a product is $58, and the quantity sold of the product is 4060. The price elasticity of demand is -4.6, and the price elasticity of supply is 0.7.

Find the demand curve and the supply curve for the product. (Your answer for the demand curve should be in the form Q_d = a – bP, with specific numerical values given for a and b. Your answer for the supply curve should be in the form Q_s = c + dP, with specific numerical values given for c and d.)

Answer 1

(a) Finding the demand curve equation:

Qd = a - bP

where a is the value of Qd when P is 0

-b is slope of demand curve.

=> ΔQd / ΔP = -b

---

Step 1: Find the value of b

Price elasticity of demand = (ΔQd/ΔP) * (P/Qd)

=> -4.6 = (ΔQd / ΔP) * (58 / 4060)

=> (ΔQd / ΔP) = -4.6(4060 / 58)

=> (ΔQd / ΔP) = -322

--

ΔQd / ΔP = -b

=> -b = -322

=> b = 322

----

Step 2: Find the value of a

Qd = a - bP

=> Qd = a - 322*P

Put P = 58 & Qd = 4060 and solve for a

=> 4060 = a - 322 (58)

=> 4060= a - 18676

=> a = 18676 + 4060

=> a = 22736

-------------

So, Qd = a - bP

=> Qd = 22736 - 322 *P (demand equation)

----------------------------------------------

(b)

Finding the supply curve equation:

Qs = c+ dP

where c is the value of Qs when P is 0

d is slope of supply curve.

=> ΔQs / ΔP = d

---

Step 1: Find the value of d

Price elasticity of supply = (ΔQs/ΔP) * (P/Qs)

=> 0.7 = (ΔQs / ΔP) * (58 / 4060)

=> (ΔQs / ΔP) = 0.7*(4060 / 58)

=> (ΔQs / ΔP) = 49

--

ΔQs / ΔP = d

=> d = 49

----

Step 2: Find the value of c

Qs = c +dP

=> Qs = c + 49P

Put P = 58 & Qs = 4060 and solve for c

=> 4060 = c + 49(58)

=> 4060 = c + 2842

=> c = 4060 - 2842

=> c = 1218

-------------

So, Qs = c + dP

=> Qs = 1218 + 49P (Supply equation)

----------------------------------------------

Note: At equilibrium point; Qd = Qs = Q = 4060 and P =$58

Please hit the like button :)