Use "Duopoly Rising MC.xlsm" for these exercises. Parameters need to be initially set so that the inverse demand function is P = 500 - 5 (Q₁ + Q₂). Firm 1 and Firm 2 have, initially, identical marginal cost functions ofMC₁ = 5Q₁ and MC₂ = 5Q₂. Enter these appropriate parameter values.

I. Assume, initially, that Firm 1 is in a monopoly position. We do so by setting cell B18 to zero on the Firm 1 tab. We see what Firm 1 elects to produce in cell B22, given Firm 2's choice of zero.

a. What is Firm 1's output level and profit? (Read from Firm 1 worksheet, with Q₂=0)

Firm 1 Output_______ B22

Firm 1 Profit________ B21

b. {Select "Transfer Q1 Value to Firm 2" on Sheet Firm 1} What is Firm 2's output response given Firm 1's output level in (a)? (Read from Firm 2's worksheet, down the column associated with Firm 1's output level, find maximum tabled profit for Firm 2 in that column and read the output level in that corresponding row.)

Firm 2 output response given Firm 1's output in (a) __________

Firm 2 Profit___________

c. {Select "Transfer Q2 Value to Firm 1" on Sheet Firm 2} Given Firm 2's output response, what output level does Firm 1 then select? (Take Firm 2's output level from (b) as given and examine the Firm 1 worksheet for the Q1 that maximizes profit taking Firm 2's output level as given.)

Firm 1's output response given Firm 2's output in (b) __________

Firm 1 Profit___________

II. This interaction continues until neither firm can improve its position by changing output. This you can see by iterating on the "Transfer values" key presses. The resulting equilibrium output levels is the Cournot solution.

a. What are the approximate Q₁ and Q₂ values in the Cournot solution? (Approximations at Resolution value of 1, resulting in an Increment=0.5 will suffice.

Q₁ Cournot Solution__________

Q₂ Cournot Solution________

b. What is the profit for each firm at the Cournot solution values? (Consult the respective Firm 1 and Firm 2 worksheets for profit levels at the designated Q values.

Firm 1 Profit__________

Firm 2 Profit__________

III. Input the equilibrium Q1, Q2 values into Firm 1's B28 and B29 cells. Examine the demand elasticities below row 42 of Firm 1.

Industry Demand Elasticity______

Firm 1 Elasticity_______

Firm 2 Elasticity_______

T/F This result corresponds to the formula E_f= N*E_m, where "f" stands for the representative firm, "m" for the market, and N is the number of firms in the market.

IV. Now assume that both firms conspire to restrict output, raise price and profit. With B28:B29 set at the Cournot equilibrium on the Firm 1 worksheet, input negative values in B34 in 0.5 increments to find the value of Firm 1 output that maximizes conspiratorial profit for Firm 1. Firm 2 changes are identical and automatic with inputs to B34.

What are the conspiratorial outputs and industry output {B37&B38} that maximizes the profits of this illegal cabal?

Firm 1 Output ___________

Firm 2 Output___________

Total Output____________

What is the profit of each firm and industry profit?

Firm 1 Profit ________

Firm 2 Profit_________

Total Industry Profit___________

V. Firm 1 cheats, raising its output level while trying to convince Firm 2 to staying constant with its level of output from IV above. "I don't know what happened. Demand just seemed to collapse." {These values will have to be read from the tables."}

Firm 1's optimal "cheating" output level________

Firm 1's profit________

Firm 2's profit________

VI. Now assume that Firm 2 has an increase in its marginal costs such that the MC₂ is = 10 Q₂. Input the value of "10" on the Firm 1 worksheet, cell B7. MC₁=5Q₁ and MC₂=10Q₂ for remaining problems.

What are the new Cournot solution quantities and industry output?

Firm 1 Output ___________

Firm 2 Output___________

Total Output____________

What is the profit of each firm?

Firm 1 Profit ________

Firm 2 Profit_________

Total Industry Profit___________

Input the equilibrium Q1, Q2 values into Firm 1's B28 and B29 cells. Set B34 to zero, so that profit levels can be read directly. Examine the demand elasticities below row 42 of Firm 1.

Firm 1 Elasticity________

Firm 2 Elasticity________

Compute the "weighted average" of these elasticities, using the share of output of each firm, shown to the right, as weights, and divide the result by the number of firms, 2.

T/F Wow! The industry elasticity of demand is the weighted average of the firm level elasticities, using Q's as the weights, and dividing by the number of firms.

VII. Firm 1, the cost leader, engages in industrial espionage and learns of Firm 2's response function. It chooses its output and leaves the "dregs" for Firm 2. What output levels result? (Examine the Firm 1 Stackelbergworksheet and find the output level for Firm 1 that maximizes profit. This yields Q₁. Then turn to the Firm 2 worksheet and find the profit max output level given the "leader's" choice of output.)

a. What are the profit maximizing outputs and industry output?

Firm 1 Output ___________

Firm 2 Output___________

Total Output____________

b. What is the profit of each firm and industry profit?

Firm 1 Profit ________

Firm 2 Profit_________

Total Industry Profit___________

VIII. Firm 1 decides to buy Firm 2 even with its higher marginal costs. Of course, it will now be a monopoly. The Joint Profit worksheet identifies total profits for the merged firm given values of Q₁ and Q₂. In the Joint Profit worksheet, input "22" into D1, "10" into C3. Choose resolution level 4 in A10. This yields more finite comparisons.

a. What output level does it choose to operate each of its plants and what is the resulting profit? (Consult the Joint Profits worksheet to obtain the answers)

Plant 1 Output ___________

Plant 2 Output___________

Total Output____________

b. What is the resulting profit with the firm now in a monopoly position?

Monopoly Profit___________

c. Compute the values of MC for each plant at their respective Q values, now that they are merged. Answer the following"

Firm 1 MC: 5 Q₁ = ___________

Firm 2 MC: 10 Q₂ = ___________

Marginal Revenue at combined output: _____________MR=500 - 10*(Q1+Q2)

T/F Maximal profit is attained by equalizing the marginal costs and setting them equal to MR for combined output.

IX. Considering the results in VI.-VIII. with the differential MC's, which outcome is best from a social welfare perspective? That is, which form of market organization --Cournot competitive, C; Stackleberg, S; merged Monopoly, M--yields the highest output and, thus, lowest prices? Rank them below:

Best _______________________

Next _______________________

Worst _____________________