| \[ \begin{array}{c} \mathop {Max}\limits_{\scriptstyle {\rm{\lambda }}_{\rm{R}} {\rm{, \lambda }}_{\rm{B}} {\rm{, \lambda }}_{\rm{M}} {\rm{,}} \atop \scriptstyle {\rm{\sigma }}_{{\rm{1B}}} {\rm{, \sigma }}_{{\rm{1M}}} {\rm{, \sigma }}_{{\rm{2B}}} {\rm{, \sigma }}_{{\rm{2M}}} } \pi = P_L \left( {\sigma _{LB} + \sigma _{LM} + \Sigma _{ - L} } \right)(\sigma _{LB} + \sigma _{LM} ) - C_B \sigma _{LB} - C_M \sigma _{LM} \\ + P_H \left( {\sigma _{HB} + \sigma _{HM} + \Sigma _{ - H} } \right)(\sigma _{HB} + \sigma _{HM} ) - C_B \sigma _{HB} - C_M \sigma _{HM} \\ + \lambda _R r - \lambda _B F_B - \lambda _M F_M \\ \end{array} \] Return to document
\[ \lambda _R^* = \Lambda - \frac{{(\alpha - C_M )}}{{(N + 1)\beta }}F_B - \frac{{\left( {\varepsilon - F_M (1 + r)} \right)}}{{(N + 1)\beta }}F_M - \frac{{\left\{ {2(C_M - C_B ) - (F_B - F_M )} \right\}}}{{(N + 1)\beta }}(F_B - F_M ) \] Return to document
\[ \int\limits_0^{\sigma _{LB} + \sigma _{LM} } {P_L \left( \sigma \right)d\sigma } + \int\limits_0^{\sigma _{HB} + \sigma _{HM} } {P_H \left( \sigma \right)d\sigma } - C_B \left( {\sigma _{LB} + \sigma _{HB} } \right) - C_M \left( {\sigma _{LM} + \sigma _{HM} } \right) + \lambda _R r - \lambda _B F_B - \lambda _M F_M \] Return to document
Figure 3 displays the cycling of both outputs and prices in Session 4 around the Cournot benchmarks for both Markets L and H. Price is plotted against the axis on the left, and output is plotted against the axis to the right. A single, horizontal line indicates the Cournot benchmark of (price, output) = (200, 24) for Market H, and a single dashed line indicates the Cournot benchmark of (100, 18) for Market L. The time series of both prices and outputs do not "converge" to the benchmarks, although they do line up with the benchmarks at different times during the session. What is striking, however, are not the time series but the averages of these quantities, especially the averages of the outputs. Return to document
Figure 4 shows the decline in producer surplus over time to the Social Optimum level (the dashed line). It then oscillates in a single period between the Social Optimum and Cournot benchmarks, recalling a "sawtooth pattern." Retail Gasoline markets operate in such a manner, with the rate of increase far exceeding the succeeding rate of decline to previous levels. Return to document
Figure 5 shows total surplus and consumer surplus in six experimental sessions. In the first three sessions, the consumer surplus level realized in the experiment oscillates above and below the theoretical level of consumer surplus that would be realized in a Cournot game. Total surplus achieved, however, is very close the theoretical total surplus expected from a Cournot setting. In the last three sessions, the Cournot and total surplus levels are markedly higher than the first three sessions, and the realized consumer surplus continues to range above and below the theoretical prediction. Total suplus, however, appears to fall short of the Cournot level more often than under the previous treatment condition. Return to document
\[ \begin{array}{c} L = P_L \left( {\sigma _{LB} + \sigma _{LM} + \Sigma _{ - L} } \right)(\sigma _{LB} + \sigma _{LM} ) - C_B \sigma _{LB} - C_M \sigma _{LM} \\ + P_H \left( {\sigma _{HB} + \sigma _{HM} + \Sigma _{ - H} } \right)(\sigma _{HB} + \sigma _{HM} ) - C_B \sigma _{HB} - C_M \sigma _{HM} \\ + \lambda _R r - \lambda _B F_B - \lambda _M F_M \\ + \mu (\Lambda - \lambda _R - \lambda _B F_B - \lambda _M F_M ) \\ + \mu _R \lambda _R + \mu _B \lambda _B + \mu _M \lambda _M \\ + \mu _{LB} (\lambda _B - \sigma _{LB} ) + \mu _{LM} (\lambda _M - \sigma _{LM} ) + \mu _{HB} (\lambda _B - \sigma _{HB} ) + \mu _{HM} (\lambda _M - \sigma _{HM} ) \\ + \gamma _{LB} \sigma _{LB} + \gamma _{LM} \sigma _{LM} + \gamma _{HB} \sigma _{HB} + \gamma _{HM} \sigma _{HM} \\ \end{array} \] Return to document
\[ \left( {F_B - F_M } \right)\left( {1 + r} \right) - \left( {C_M - C_B } \right) = \left( {\mu _{HB} + \gamma _{LB} + \mu _B } \right) - \left( {\mu _{HM} + \gamma _{LM} + \mu _M } \right) - \left( {F_B - F_M } \right)\mu _R > 0 \] Return to document
\[ \left( {F_B - F_M } \right)\left( {1 + r} \right) - \left( {C_M - C_B } \right) = \left( {\mu _{LB} + \gamma _{HB} + \mu _B } \right) - \left( {\mu _{LM} + \gamma _{HM} + \mu _M } \right) - \left( {F_B - F_M } \right)\mu _R > 0 \] Return to document
\[ 2\left( {C_M - C_B } \right) - \left( {F_B - F_M } \right)\left( {1 + r} \right) = \left( {\gamma _{LM} + \gamma _{HM} + \mu _M } \right) - \left( {\gamma _{LB} + \gamma _{HB} + \mu _B } \right) + \left( {F_B - F_M } \right)\mu _R > 0 \] Return to document
\[ \lambda _B^* = \sigma _{HB}^* = \sigma _{LB}^* = \frac{{\left( {\alpha - C_M } \right) + 2(C_M - C_B ) - (F_B - F_M )(1 + r)}}{{(N + 1)\beta }} \\ > \frac{{2(C_M - C_B ) - (F_B - F_M )(1 + r)}}{{(N + 1)\beta }} > 0 \] Return to document
\[ \lambda _M^* = \sigma _{HM}^* = \frac{{\left( {\varepsilon - F_B (1 + r)} \right) + 2\left\{ {(F_B - F_M )(1 + r) - (C_M - C_B )} \right\}}}{{(N + 1)\beta }} \\ > \frac{{2\left\{ {(F_B - F_M )(1 + r) - (C_M - C_B )} \right\}}}{{(N + 1)\beta }} > 0 \] Return to document
\[ \lambda _R^* = \Lambda - \lambda _B^* F_B - \lambda _M^* F_M \\ = \Lambda - \frac{{(\alpha - C_M )}}{{(N + 1)\beta }}F_B - \frac{{\left( {\varepsilon - F_M (1 + r)} \right)}}{{(N + 1)\beta }}F_M - \frac{{\left\{ {2(C_M - C_B ) - (F_B - F_M )} \right\}}}{{(N + 1)\beta }}(F_B - F_M ) \] Return to document
This form shows three tables next to each other below the form's title. For simplicity each table will be shown by itself. Row numbers are shown in parenthesis (). | Participant Number: | Market Period: |
How many certificates will you buy? (Circle One) Left-hand: (0) 0 for 0 francs, (1) 1 for 30 francs, (2) 2 for 60 francs (circled), (3) 3 for 90 francs, (4) 4 for 120 francs . . . (15) 15 for 450 francs, (16) 16 for 480 francs Right-hand: (0) 0 for 0 francs, (1) 1 for 70 francs, (2) 2 for 140 francs, (3) 3 for 210 francs, (4) 4 for 280 francs (circled) . . . (15) 15 for 1050 francs, (16) 16 for 1120 francs MARKET 1: How many certificates will you redeem in Market 1? (Circle One) Left-hand: (0) 0 for a fee of 0 francs, (1) 1 for a fee of 50 francs (circled), (2) 2 for a fee of 100 francs, (3) 3 for a fee of 150 francs, (4) 4 for a fee of 200 francs . . . (15) 15 for a fee of 750 francs, (16) 16 for a fee of 800 francs Right-hand: (0) 0 for a fee of 0 francs, (1) 1 for a fee of 10 francs, (2) 2 for a fee of 20 francs, (3) 3 for a fee of 30 francs, (4) 4 for a fee of 40 francs (circled) . . . (15) 15 for a fee of 150 francs, (16) 16 for a fee of 160 francs MARKET 2: How many certificates will you redeem in Market 2? (Circle One) Left-hand: (0) 0 for a fee of 0 francs, (1) 1 for a fee of 50 francs, (2) 2 for a fee of 100 francs (circled), (3) 3 for a fee of 150 francs, (4) 4 for a fee of 200 francs . . . (15) 15 for a fee of 750 francs, (16) 16 for a fee of 800 francs Right-hand: (0) 0 for a fee of 0 francs, (1) 1 for a fee of 10 francs, (2) 2 for a fee of 20 francs, (3) 3 for a fee of 30 francs (circled), (4) 4 for a fee of 40 francs . . . (15) 15 for a fee of 150 francs, (16) 16 for a fee of 160 francs Return to document
This form shows three tables next to each other below the form's title. For simplicity each table will be shown by itself. | Participant Number: | Market Period: |
ACCOUNTING SHEET EXPENSES Purchases (francs) Left-hand Certificates_____ Right-hand Certificates_____ Total Purchases (Less than 1001 francs )_____ Redemption Fees (francs) Market 1: Left-hand Certificates_____ Right-hand Certificates_____ Total Redemption Fees_____
Market 2: Left-hand Certificates_____ Right-hand Certificates_____ Total Redemption Fees_____ Total Purchases (Less than 1001 francs ) + Market 1 Total + Market 2 Total = TOTAL EXPENSES:_____ REVENUE Number of Certificates Redeemed Market 1: Left-hand + Right-Hand = Total Number Redeemed x Redemption Values (francs) = Total Income (francs)
Market 2: Left-hand + Right-Hand = Total Number Redeemed x Redemption Values (francs) = Total Income (francs) TOTAL REVENUE from the REDEMPTION OF CERTIFICATES: Market 1 Total Income (francs) + Market 1 Total Income (francs) PROFIT from the Redemption of Certificates = REVENUE minus EXPENSES: Francs not used to purchase certificates x 1.2: Payoff = PROFIT plus (Unused FRANCS x 1.2): Return to document | 
U.S. Department
of Justice
