1. You manage a firm that is a price taker. The market price for you good is $12
ID: 1165036 • Letter: 1
Question
1. You manage a firm that is a price taker. The market price for you good is $120.00. You marginal cost is MC= 25 + 0.5Q and your fixed cost is $500.00.
a) Determine your profit maximizing output.
b) What is your Total Revenue?
c) What is your Average Variable Cost?
d) What is your Variable Cost?
e) What is your Total Cost?
f) What is your Profit?
2.) You mange a price setting firm facing a demand function given as P = 500 - 0.25Q. Your Marginal Cost Function is MC = 100 + 0.5Q and your fixed costs are FC = $5000.00.
a) What is your profit maximizing output?
b) What is your profit maximizing Price?
c) repeat parts b-f from problem #1
Explanation / Answer
Ans 1)
Firm is Price Taker then it is not Monopoly for sure ( Monopoly is Pricec Maker)
Price =Marginal Cost
Price=25+0.5Q
120=25+0.5Q
95=0.5Q
Q=475
Revenue=Price *Quantity=120*475=$57000
variable cost=MC*Q
MC=d(TC)/dQ=25+0.5Q
dTC=(25+0.5Q)dQ
If we integrate both the sides then we get
VC=25Q+0.25Q^2
Now The Average Variable Cost=VC/Q=25+0.25Q
Total Cost=FC+VC=500+25Q+0.25Q^2
Profit=(Price*Q-(FC)-25Q-0.25Q^2=57000-500-25(475)-0.25(475)^2=-11781.25
Ans 2)
Price Setting Firm is Mnopoly then Profit Maximising condition is
MR=MC
Revenue=P*Q=500Q-0.25Q^2
MR=500-0.5Q and MC=100+0.5Q
500-0.5Q=100+0.5Q
400=Q this is profit maximising output and Profit maximising price =500-0.25(400)=400
Revenue=P*Q=(400)^2=160000
Average Variabe Cost=100+0.25Q
Variable Cost=100Q+0.25Q^2
Total Cost=VC=FC=5000+100Q+0.25Q^2
Profit=160000-5000-100(400)+0.25(400^2)=$155000
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