The Fragle Firm faces the following cost function Q TC 0 60 1 82 2 97 3 109 4 12
ID: 1187098 • Letter: T
Question
The Fragle Firm faces the following cost function
Q TC
0 60
1 82
2 97
3 109
4 125
5 146
6 171
7 203
8 240
9 282
10 427
11 477
12 533
1) Assume the Frangle Firm can sell all of the output it wants at a price of $55. How much should it produce and sell if tis is to maximize its profit?
2) If the price falls $40, how much should the firm produce and sell if it wants to maximize profits? What are the maximum profits?
3) Now assume that the first unit can be sold for a price of $80 and that the firm must lower its price by $2 for each additional unit it sells. What is the new profit maximizing levelof output and the new maximum profit level (i.e. it sells the fir unit for $80 and it sells 2 units for $78?
Show all work!!!
Explanation / Answer
I will tell you the way to get to solution ;
Plot TC Vs Q ;
you will get TC = f(Q) ;
Total Revenue = Price*Q ;
1) Profit P = TR - TC = 55Q - f(Q) ;
dP / dQ = 0 ;
f'(Q) = 55 ;
get Q
2) f'(Q) = 40 ;
get Q
Profit = 40*Q - f(Q)
3) Plot Revenue v/s Q ;
Q=1 TR = 80 ;
Q= 2 TR = 80 + 78
Q= 3 TR = 80 +78 +76 ;
you will get TR = y(Q) ;
Profit P = TR - TC = y(Q) - f(Q)
dP/dQ = 0
y'(Q) = f'(Q) ;
solve to get Q ;
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