Hướng dẫn Giải bài tập Kinh tế vi mô, Phần 2, TS. Phan Thế Công

[@jamesp9843]

Given: Qs = 0.5(P - 4) -> P = 2Qs + 4. TFC = 225.
MC = dTC/dQ = dTVC/dQ. ∫MC = ∫dTVC/dQ - > ∫MC*dQ = ∫dTVC = TVC
Perfect competition: P = MC.
1. MC = 2Q + 4
TVC = ∫MC*dQ = ∫(2Q + 4)dQ = Q^2 + 4Q
TC = TVC + TFC = Q^2 + 4Q + 225
AFC = TFC/Q = 225/Q
ATC = TC/Q = (Q^2 + 4Q + 225)/Q = Q + 4 + 225/Q
AVC = TVC/Q = (Q^2 + 4Q)/Q = Q + 4
2. P = ATC
2Q + 4 = Q + 4 + 225/Q
Q^2 = 225 -> Q = 15.
P = 2Q + 4 = 2*15 + 4 = 34.
Shutdown point: P ≤ AVCmin
P = AVCmin = MC = 2Q + 4
Shutdown means Q = 0. P = 2Q + 4 = 2(0) + 4 = 4. The loss is TFC = 225.
3. P = 2Qs + 4 -> 16 = 2Q + 4 -> 12 = 2Q -> Q = 6.
TR = P*Q = 16 * 6 = 96
TC = Q^2 + 4Q + 225 = 62 + 4(6) + 225 = 285
Profit = Ꙥ = TR - TC = 96 - 285 = -189.
4. P = 2Qs + 4 -> 68 = 2Q + 4 -> 64 = 2Q -> Q = 32.
TR = P*Q = 68 * 32 = 2176
TC = Q^2 + 4Q + 225 = 322 + 4(32) + 225 = 1377
Profit = Ꙥ = TR - TC = 2176 - 1377 = 799.
5. Tax = 2. When there is a tax, lower quantity sold.
New TC = TC + t*Q = Q^2 + 4Q + 225 + 2*Q = Q^2 + 6Q + 225
MC = dTC/dQ = 2Q + 6
ATC = TC/Q = (Q^2 + 6Q + 225)/Q = Q + 6 + 225/Q.
AVC = TVC/Q = (Q^2 + 6Q)/Q = Q + 6
P = MC = 2Q + 6 -> 16 = 2Q + 6 -> 10 = 2Q -> Q = 5.
TR = P*Q = 16 * 5 = 80
TC = Q^2 + 6Q + 225 = 52 + 6(5) + 225 = 280
Profit = Ꙥ = TR - TC = 80 - 280 = -200. Lower quantity sold of 5 and bigger loss of 200.
P = MC = 2Q + 6 -> 68 = 2Q + 6 -> 62 = 2Q -> Q = 31.
TR = P*Q = 68 * 31 = 2108
TC = Q^2 + 6Q + 225 = 312 + 6(31) + 225 = 1372
Profit = Ꙥ = TR - TC = 80 - 280 = 736. Lower quantity sold of 31 and smaller profit of 736.

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