SOLUTION: example problems of supply function

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Question 424121: example problems of supply function
Answer by MathLover1(20849) About Me  (Show Source):
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Supply Function indicates the relationship between the quantity of the
commodity supplied and the unit+price of the commodity.

The slope of a supply curve is usually+positive, as price
increases, quantity supplied increases and vice-versa.
The y-intercept of the supply curve (0,b) represents the lowest
price at which an item will be supplied.

Normally, we put the good’s own price and cost into the supply function.
For the previous example that we use,
Qs=g(p, wage, capital cost)
When p increases, firms/producers want to produce more goods because it will provide them with more profit. When cost increase, produce would like to reduce their supply given same capital constraint.
So,
P increases ...=>... Quantity supplied increases along the supply curve.
Wage increases (cost increases) -=>-- supply curve shift to the left for same price.
An example of supply function:
Qs=178+40p-20w-60r
where w=wage of labor, r=interest_+rate for producer’s loan
When w=5.5 and +r=1.05

Qs=178%2B40p-2%2A5.5-60%2A1.05

=104%2B40p
Suppose w=10, then
Qs=178%2B40p-2%2A8-60%2A1.05
=99%2B40p
So when wage+rises, supply curve shifts to the left, which means that for a given price, producers will supply less goods than before.