Answer to Question #166267 in Microeconomics for jack

Question

At a price of $8 per unit, Gadgets Inc. is willing to supply 19,000 gadgets, while United Gadgets is willing to supply 16,000 gadgets. If the price were to rise to $10 per unit, their respective quantities supplied would rise to 28,000 and 22,000. If these are the only two firms supplying gadgets, what is the elasticity of supply in the market for gadgets?

-1.59

0.63

1.4

1.59

2.22

Answer 1

Price elasticity of supply is given by:

$E_s=\dfrac{\Delta Q}{\Delta P}\times \dfrac{\bar P}{\bar Q}$

At P=$8, the total supply is Q=19000+16000=35000.

At P=$10, the total supply is equal to Q=28000+22000=50000

Therefore:

$\dfrac{\Delta Q}{\Delta P}=\dfrac{50000-35000}{10-8}=7500\\[0.3cm] \bar Q=\dfrac{35000+50000}{2}=42500\\[0.3cm] \bar P=\dfrac{10+8}{2}=\$9$

Therefore, the price elasticity of supply is equal to:

$E_s=7500\times \dfrac{9}{42500}\\[0.3cm] E_s\approx \boxed{1.59}$