Question

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Let us assume that a product has the following demand and supply functions displayed below: Q 120-2P Q,--150+3P Calculate the price elasticity of demand and price elasticity of supply for the point of market equilibrium. Explain the obtained result.

Answer 1

In equilibrium Qd=Qs

120-2p=-150+3p

120 +150=3p+2p

270=5p

270/5=p

P=54

Solve for Q

120-2p

120-2(54)

12 we know that equilibrium price is 54and equilibrium quantity is 12

Qs=-150+3p

-150+3(54)

-150+162=-12 so we know that equilibrium price is 54, and equilibrium quantity is - 12

Price Elasticity of demand =%change in demand /%change in price

Price Elasticity of supply =%change in supply /%change in price

The point elasticity of demand formula is

Elasticity of Demand = (-1/slope)(P/Qd)
and the point elasticity of supply formula is
Elasticity of Supply = (1/slope)(P/Qs)
At the equilibrium quantity and price we know (Q, P) = (54, 12). We also have the demand and supply equations, but they are not in slope-intercept form. So, rewriting the two equations in slope-intercept form we have:
Demand Equation: P =chnge quality /chnge price=-2/1
Supply Equation: P = 3/1=3
Now, we are ready to use the point elasticity formulas:
Point Elasticity of Demand = [(54/12)*(-2)=-9hence, demand is less than elastic at the point of equilibrium in this market)
Point Elasticity of Supply = [54/12*(3)=13.5hrnce supply is more elastic at point of equilibrium in this market