Question Tag: Elasticity of Demand

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  • 8 Marks

QT – Nov 2018 – L1 – Q2c – Elements of Calculus

Determine and interpret the elasticity of demand at different price levels for kente strips.

Due to changes in market conditions, the company finds the demand qq (in thousands) for their kente strips to be at a price of GH¢p per kente strip.

Required:
(i) Determine the elasticity of demand when the price is GH¢5 and when the price is GH¢15 per kente strip. (6 marks)
(ii) Comment on your results in (i). (2 marks)

i)

First, find the derivative of the demand function q = 400 −

Now calculate the elasticity at the given prices:

When p = 

PED =

 

 

When p = 15  we have :

 

PED =

(ii) Comment on the results:

When p = 5 the demand is inelastic as the elasticity is less than 1 in absolute value, indicating that a change in price will result in a smaller percentage change in quantity demanded.
When p = 15, the demand is elastic, as the elasticity is greater than 1 in absolute value, indicating that a change in price will result in a larger percentage change in quantity demanded.

  • 10 Marks

QT – Nov 2018 – L1 – Q2b – Elements of Calculus

Determine the price and quantity that maximize revenue and profit, and compute the maximum profit for Renes Trading Company.

Renes Trading Company sells qq kente strips per month at pp Ghana Cedis per kente strip. The demand function for kente strips is given by p=300−0.02qp = 300 – 0.02q. The kente strips cost GH¢30 per strip to manufacture. There are fixed costs of GH¢9,000 per month.

Required:
(i) Determine the price per kente strip that will maximize revenue. (4 marks)
(ii) Determine the quantity where profit is maximized. (4 marks)
(iii) Calculate the maximum profit. (2 marks)

(i)

 

ii)

 

iii)

 

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