Question

A supplier supplies 50 T-shirts when the price is R60 per t-shirt and 90 t-shirts when the price is R110 per t-shirt.

a). Determine the equation of the supply function as a function of q?

b). How many additional t-shirts are sopplied for each successive R1 increase in price?

c). How many t-shirts are sopplied when the price is R85?

d). What is the price when 120 t-shirts are sopplied?

Answer 1

a)Supply equation is written as;

$P_{s}=mQ+b$

where m is the slope of supply curve.

m=$\frac{\delta P}{\delta Q}=\frac{110-60}{90-50}=1.25$

Inserting the supply of 50 T-shirts at a price of R60 per t-shirt in the supply equation to get b;

$60=1.25\times50+b$

$b=-2.5$

$\therefore$ the supply equation becomes;

$P_{s}=1.25Q-2.5$

b). Additional t-shirts supplied for each successive R1 increase in price will be?

For every R1 increase in price;

$1=1.25Q-2.5$

$Q=\frac{3.5}{1.25}=2.8$

c) T-shirts supplied when the price is R85;

$85=1.25Q-2.5$

$Q=\frac{87.5}{1.25}=70$ t-shirts

d) Price when 120 t-shirts are supplied;

$P_{s}=1.25Q-2.5$

$P_{s}=1.25\times120-2.5=R147.5$