Answer to Question #265013 in Microeconomics for Serikisulaimon

Question #265013

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?



1
Expert's answer
2021-11-14T17:36:44-0500

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"




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