Eco 550 Week7 Check Your Understanding

Topics: Game theory, Nash equilibrium, Decision theory Pages: 3 (637 words) Published: May 27, 2013
Check Your Understanding Week 7
o Chapter 13: Problems 2, 13, and 15

2. a. Player A does not have a dominant strategy. Its optimal decision depends on what player B does. If player B chooses strategy 1, then player A does best by also choosing strategy 1; however, if player B chooses strategy 2, then player A's optimal choice is also strategy 2.

b.Player B likewise does not have a dominant strategy. Its optimal decision depends on what player A does. If player A chooses strategy 1, then player B does best by also choosing strategy 1; however, if player A chooses strategy 2, then player B's optimal choice is also strategy 2.

13. Introduce Picture CD since Sony's best reply response will be to increase advertising and Kodak will then price moderately yielding {$610 Kodak, $590 Sony}.

15. The NE and SW cells are the only two pure equilibria (both Nash equilibria). The two graduate students should coordinate their response (also known as collude) so as to avoid the occurrence of NW cell and SE cell outcomes. Perhaps flip for who will approach Russell Crowe, or alternate. Note: This problem is re-crafted from a scene in the 2001 movie, “A Beautiful Mind,” that explored the life and mind of John Nash.

o Chapter 14: Problems 3(b, c, d), 5(a, b, c), and 8(a, b, c) 3.Two classes of freight for the American Export-Import Shipping Company.

a.Demand functions: P1 = 100 − 2Q1 for manufactured goods and P2 = 80 − Q2 for semi-manufactured goods.
Revenue function: TR = (100 Q1 – 2 Q12) + (80 Q2 – Q22) Cost function: TC = 20 + 4(Q1 + Q2)

Profit function: π = TR-TC = −20 + 96Q1 + 76Q2 − 2Q12 − Q22

b. Find where ∂π/∂Q1 = 96 − 4Q1 = 0 and ∂π/∂Q2 = 76 − 2Q2 = 0
Q1* = 24 tons; P1* = $52/unit and also Q2* = 38 tons; P2* = $42/unit.

c. TR = 100Q1 − 2Q12 + 80Q2 − Q22
MR1 = ∂(TR)/∂Q1 = 100 − 4Q1 = 100 − 4(24) = $4/unit
MR2 = ∂(TR)/∂Q2 = 80 − 2Q2 = 80 − 2(38) = $4/unit

d. π * = −20 + 96(24) + 76(38) −...
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