Question

Given the following demand function for beef (kg), P = 200 – 5Q i) By how much would the price have to fall for consumers to be willing to buy 1 more kg of beef per day? [5 marks] ii) If the price decreases by N$0.9, by how much will the demand changed?

Answer 1

Solution:

i). Derive the inverse demand function:

P = 200 – 5Q

5Q = 200 – P

Q = $40 - \frac{P}{5}$

When the beef is 1 kg, the price will be as follows:

Q = $40 - \frac{P}{5}$

1 = $40 - \frac{P}{5}$

5 = 40 – P

P = 40 – 5

P = 35

Consumers will pay N$35 for a kg of beef

When an extra beef of kg is added, the price will be as follows:

Q = $40 - \frac{P}{5}$

2 = $40 - \frac{P}{5}$

10 = 40 – P

P = 40 – 10

P = N$30

Price change = 35 – 30 = N$5

The price will have to fall by N$5 for the consumers to be willing to buy 1 more kg of beef per day.

 

ii). First derive demand at previous price of N$35:

Q = $40 - \frac{P}{5}$

Q = $40 - (\frac{35}{5} )$

Q = 40 – 7

Q = 33

Then derive the demand at the current price of N$34.1:

That is: 35 – 0.9 = N$34.1

Q = $40 - \frac{P}{5}$

Q = $40 - (\frac{34.1}{5} )$

Q = 40 – 6.82

Q = 33.18

The demand will change by: 33.18 – 33 = 0.18kg

The demand will increase by 0.18kg