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Supply Function and Profit Question

Hi, I am fairly new to economics, and I have been having trouble with the following question. I would appreciate any help! Thank you!



Sarah’s firm produces granola bars with a fixed cost of 10 (this cost is already sunk). Her variable cost function is given by

VC(Q) = Q2 + 2Q

A) Assuming the Market for granola bars is competitive, derive Sarah's supply function.

B) What is Sarah’s surplus if the market price is 6? What is her profit? Does she want to stay in this market? Explain.




Sarah’s firm produces granola bars with a fixed cost of 10 (this cost is already sunk). Her variable cost function is given by

VC(Q) = Q2 + 2Q

A) Assuming the Market for granola bars is competitive, derive Sarah's supply function.

TC= Q^2 +2Q + 10

MC= 2Q+2

Setting MC=P, we get

P= 2Q+2
or, Q= P/2 - 1 (Supply function)

B) What is Sarah’s surplus if the market price is 6? What is her profit? Does she want to stay in this market? Explain

If market price is 6,
demand= P/2-1= 6/2-1=2

Total revenue = 2*6 = 12
Total cost = Q^2 +2Q = 4 + 4 + 10= 18(fixed costs are sunk)
Profit = -6

TR = Q*P= Q*(2Q+2)= 2Q^2+2Q
MR= 4Q+2
At Q=2, MR= 10
AVC= Q+2=2+2=4
Hence, MR>AVC

A firm shuts downs at the point where MR<AVC at the profit maximizing output. Hence, Sarah will remain in the market.

Source: http://tutorteddy.com/free_economics_homework_help.php

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