A firm has the following marginal cost function:
MC(y)=2y |
and fixed costs equal to $16 . If the price of y changes from $8 to $15 what is the change in the firm's profits? (Change equals new minus old) Round your answer to 4 decimal places.
We know that marginal cost is the derivative of total cost function. So, in reverse, the total cost function would be the integration of the marginal cost. So, this means
Total cost=
=y^{2}+constant,
and this contant is the fixed cost. So,
Total cost=y^{2}+16.
The company would produce at such a level which maximizes profit, in other words where MC=MR. MR is nothing but price. So,
When price is 8,
2y=8, y=4.
Revenue at y=4
Revenue=price*quantity.
Revenue when y=4 is 4*8=32. Cost at this level is
4^{2}+16=32.
Hence, profit=revenue-cost=32-32=0.
When price=15,
2y=15
y=7.5.
Revenue at this level= 7.5*15=112.5.
Total cost at this level= 7.5^{2}+16=72.25.
Profit at this level=Revenue-Cost=112.5-72.25=40.25
So, change in firm's profits when price changes from 8 to 15=40.25-0=$40.25
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