Question

$\huge{\underline{\underline{\bf{\red{Question :-}}}}}$
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☆ The market price of a good changes from ₹5 to ₹20. As a result, the quantity supplied by the firm increases by 15 units. The price elasticity of supply is 0.5. Find the initial and final output levels of the firm.
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Answer 1

Question:-

The market price of a good changes from ₹5 to ₹20. As a result, the quantity supplied by the firm increases by 15 units. The price elasticity of supply is 0.5. Find the initial and final output levels of the firm.

Given:-

• Elasticity of supply (es)= 0.5
• Initial price (P1) = Rs 5
• Final price (P2) = Rs 20

To Find:-

• the initial and final output levels of the firm

Solution:-

$\large{ \sf{ ΔP = P_{2} - P_{1}}}$

$\sf \large{ΔP = 20 - 5}$

$\large{ \sf{ ΔP = 15}}$

$\large{ \sf{ΔQ = 15}}$

$\boxed{ \sf{ \green{ \large{ e_{s} =  \frac{ΔQ}{ΔP} x\frac{ P_{1}}{ Q_{1} } }}}}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: 0.5 = \frac{15}{15} \times \frac{5}{Q _{1} } }$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: 0.5 = \frac{5}{Q _{1} } }$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: {Q _{1} = \frac{5}{0.5}} }$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: {Q _{1} = 10 \: units} }$

Now,

• Initial quantity = 10 units
• Final quantity,Q2 = ∆Q + Q1 = 15 + 10 = 25 units

Hence:-

• Initial quantity = 10 units
• Final quantity = 25 units

Answer 2

Answer:

★ Question :-

The market price of a good changes from ₹5 to ₹20.As a result, the quantity supplied by a firm increases by 15 units. The price elasticity of the firm's supply curve is 0.5.Find the initial and final levels of the firm.

concept :-

Elasticity of supply is measured as the ratio of proportionate change in the quantity supplied to the proportionate change in price.

↪elasticity of supply

= % change in quantity supplied / % change in price.

★ Answer :

Elasticity of Supply, es = 0.5

Initial Price, P1 = Rs 5

Final price, P2 = Rs 20

ΔP = P2 - P1 = 20 - 5

then ,

ΔP = 15

ΔQ = 15

es = ΔQ/ΔP x P1/Q1

$\large{ \sf{ ΔP = P_{2} - P_{1}}}$

$\sf \large{ΔP = 20 - 5}$

$\large{ \sf{ ΔP = 15}}$

$\large{ \sf{ΔQ = 15}}$

$\boxed{ \sf{ \green{ \large{ e_{s} =  \frac{ΔQ}{ΔP} x\frac{ P_{1}}{ Q_{1} } }}}}$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: 0.5 = \frac{15}{15} \times \frac{5}{Q _{1} } }$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: 0.5 = \frac{5}{Q _{1} } }$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: {Q _{1} = \frac{5}{0.5}} }$

$\large{ \rm \longmapsto \: \: \: \: \: \: \: {Q _{1} = 10 \: units} }$

Q 1 = 10units

Initial quantity = 10 units

then,

Final quantity,Q2 = ΔQ + Q1 = 15 + 10

Therefore, Q2 = 25 units

I hope it helps you!