Question:

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.  Edit

Answer: 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 MREdit