. (Adapted from Dubey, Price-quantity strategic market games, Econometrica 50 (1982), no. 1, 111-126). Consider the following markets. In each case, illustrate the market with a graphic like Figure 1, and find the competitive prices, the competitive allocations, and the total surplus. (a) v1 = v2 = 4, v3 = v4 = 3, v5 = v6 = 2, c1 = 1, c2 = c3 = 2, c4 = c5 = c6 = 2.5. (b) v1 = v2 = v3 = 4, v4 = v5 = 3, v6 = v7 = 2, c1 = c2 = 1, c3 = c4 = 1.5, c5 = c6 = 2. (c) v1 = v2 = 4, v3 = v4 = 1, c1 = 1/2, c2 = 2, c3 = c4 = 3. (d) v1 = v2 = c1 = c2 = 1. (e) v1 = v2 = 7, v3 = v4 = 5, v5 = v6 = 4, c1 = 1, c2 = c3 = 2, c4 = c5 = c6 = 3. (f) v1 = 2 v2 = v3 = 1.5, v4 = v5 = 1, c1 = c2 = c3 = 2.5, c4 = c5 = 3.

30 28 supply 26 24 = = =competitive puces_ _ _ _ thousand US$ 18 16 demand 14 12 10 2 3 4 5 6 7 8 9 10 traders Figure 1: Supply and demand for tractors, and competitive prices 21