Question

A manager believes that the supply for his product is given by the equation P= 50+(Q/100).The arc elasticity of supply as price increases from Rs 10000 to Rs 20000 is closet to

Answer 1

Solution:

Arc elasticity of supply = $=\frac{\%\;change\; in\; quantity\; supplied}{\%\; change\; in\; price}$

Find the inverse supply function:

P = 50 + Q/100

Q = 100P – 5000

When Price is Rs 10,000:

Q = 100(10,000) – 5,000 = 1,000,000 – 5,000 = 995,000

When Price is Rs 20,000:

Q = 100(20,000) – 5,000 = 2,000,000 – 5,000 = 1,995,000

% Change in quantity supplied = $\frac{Q_{2} -Q_{1}}{(Q_{2}+Q_{1})/2 } \times 100$

$\frac{1995000 -995000}{(1995000+995000)/2 } \times 100 = \frac{1000000}{1495000} \times 100 = 6.69\%$

 

% change in price = $\frac{P_{2} -P_{1}}{(P_{2}+P_{1})/2 } \times 100$

$\frac{20000 -10000}{(20000+10000)/2 } \times 100 = \frac{10000}{15000} \times 100 = 66.67\%$

 

Arc elasticity of supply = $\frac{6.69\%}{66.67\%} = 0.1$

Arc elasticity of supply = 0.1