Economics Homework
Assignment 2 Calculations
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The short-run cost function:
TC = 160,000,000 + 100Q + 0.0063212Q2
ATC = TC/Q = 160,000,000/Q + 100 + 0.0063212Q
VC = 100Q + 0.0063212Q2
FC = 160,000,000
MC = ΔTC/ΔQ = 100 + 0.0126424Q
The long-run cost function:
TC = 100Q + 0.0063212Q2
AC =100Q/Q + 0.0063212Q2/Q = 100 + 0.0063212Q
VC = 100Q + 0.0063212Q2
AVC = VC/Q = (100Q + 0.0063212Q2)/Q
Suggest substantive ways in which the low-calorie food company may use this information in order to make decisions in both the short-run and the long-run.
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From assignment 1:
Qd = 38650 – 42P
P = 38650/42 – Q/42 = 920.238 – 0.0238 Q
MC = 920.238 – 0.0476 Q
In perfectly competitive market; P = MC, therefore;
920.238 – 0.0238 Q = 100 + 0.0126424Q
820.238 = 0.0364424 Q
Q = 22507.8
P = 920.238 – 0.0238(22507.8) = 384.55
In a noncompetitive market which is the condition in assignment 2:
MR = MC
TR = P.Q = 920.238 Q– 0.0238Q2
MR = 920.238 – 2(0.0238) Q = 920.238 – 0.0476 Q
MR = MC
920.238 – 0.0476 Q = 100 + 0.0126424Q
0.0602424Q = 820.238
Q = 820.238/0.0602424 = 13,615.63 units
P= 920.238 – (0.0238 * 13,615.63) = 596.19 cents
So a higher price with lower quantity is charged in a noncompetitive market.
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Profit in assignment 1 when the market is perfectly competitive:
Profit = P.Q – TC = (384.55) (22507.8) – [160,000,000 + 100 (22507.8) + 0.006321(22507.8)2] = 8,655,374.49-165,453,005 = -156,797,630.81 which is a loss.
Using the data to find the profit in assignment 2:
Profit in the short run = P.Q – TC = (596.19) (13,615.63) – [160,000,000 + 100 (13,615.63) + 0.006321(13,615.63)2] = 8,117,502.45 – 162,533,383.99 = -154,415,881.54 (which is a loss)
Profit in the long run = P.Q – TC = (596.19) (13,615.63) – [100 (13,615.63) + 0.006321(13,615.63)2] = 8,117,502.45 – 2,533,383.99 = 5,584,118,46
What are the values of ATC and AVC at the output level of 13,615.63?
ATC = TC/Q = [160,000,000 + 100 (13,615.63) + 0.006321(13,615.63)2] / 13615.63 = 162,533,383.99 / 13615.63 = 11937.27
AVC = 2533383.99 / 13615.63 = 186.06
P = 596.19
Price is between ATC and AVC so they better to stay open in the short run.
P - ATC= 596.19 - 11937.27 = 11341.08 loss per unit
11341.08 * 13615.63 = 154415881.54 total loss if they operate
160,000,000 total loss if they shut down
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