Question

The equilibrium price for a product is $38, and the quantity sold of the product is 2280. The price elasticity of demand is -4.2, and the price elasticity of supply is 0.3. Find the demand curve and the supply curve for the product. (Your answer for the demand curve should be in the form Qd = a – bP, with specific numerical values given for a and b. Your answer for the supply curve should be in the form Qs = c + dP, with specific numerical values given for c and d.

Answer 1

General Demand Function, Qd = a - bp

where b = slope = dQ/dP

Elasticity of Demand = -4.2

(dQ/dP)*(P/Q) = -4.2

(dQ/dP)(38 / 2280) = -4.2

(dQ/dP) = -4.2 / 0.016 = -252

Demand equation: Q = a - 252P

2280 = a - 252*38

a = 11,856

Hence, demand equation: Qd = 11,856 - 252P

General Supply equation: Qs = c + dP

d = dQs/dP

Elasticity of supply = 0.3

(dQs/dP)*(P/Q) = 0.3

(dQ/dP)(38 / 2280) = 0.3

dQs/dP = 18

Qs = a + 18P

2280 = a + 18*38

a = 1596

Supply equation: Qs = 1596 + 18P

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