Question

The equilibrium price for a product is $32, and the quantity sold of the product is 1280. The price elasticity of demand is -5.2, and the price elasticity of supply is 0.9.

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

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Step 1: Find the value of b

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

=> -5.2 = (ΔQd / ΔP) * (32 / 1280)

=> (ΔQd / ΔP) = -5.2(1280 / 32)

=> (ΔQd / ΔP) = -208

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ΔQd / ΔP = -b

=> -b = -208

=> b = 208

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Step 2: Find the value of a

Qd = a - bP

=> Qd = a - 208*P

Put P = 32 & Qd = 1280 and solve for a

=> 1280 = a - 208(32)

=> 1280 = a - 6656

=> a = 1280 + 6656

=> a = 7936

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So, Qd = a - bP

=> Qd = 7936 - 208*P (demand equation)

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(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

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Step 1: Find the value of d

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

=> 0.9 = (ΔQs / ΔP) * (32 / 1280)

=> (ΔQs / ΔP) = 0.9*(1280 / 32)

=> (ΔQs / ΔP) = 36

--

ΔQs / ΔP = d

=> d = 36

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Step 2: Find the value of c

Qs = c +dP

=> Qs = c + 36P

Put P = 32 & Qs = 1280 and solve for c

=> 1280 = c + 36(32)

=> 1280 = c + 1152

=> c = 1280 - 1152

=> c = 128

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So, Qs = c + dP

=> Qs = 128 + 36P (Supply equation)

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Note: At equilibrium point; Qd = Qs = Q = 1280 and P =$32

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