// LabBertrandSpecs.swift. 8/29/2020. import Foundation class LabBertrandSpecs { let strBertrandSpecs :String = """ `` Lab Specs Bertrand Equilibrium // 0: Title // Demand function slider parameters 1000 2000 100 1000 // 1: Quantity constant -5.00 -1.00 1.00 -2.00 // 2: Quantity coefficient // Per unit cost slider parameter 50.00 150.00 5.00 100.00 // 3: Per unit costs // Price sliders 50 200 5 200 // 4: Firm A price 50 200 5 200 // 5: Firm B price `` Prob Specs ` Problem 0 Start Screen 1 - Bertrand Dynamics: Unilateral Price Increase // 0: Title // Visibility sliders: Per unit cost, Demand constant, Demand price coefficient, // Price A, Price B L L L L L // 1: Label only, Both scrollbar and label // Initial values: Per unit cost, Demand constant, Demand price coefficient, // Price A, Price B 100 1000 -2 200 200 // 2: Initial values ` Text Start // 3: Text `RED`BLDObjective:`BLD Illustrate that whenever both firms are charging the same price that exceeds per unit costs, a single firm will not raise the price unilaterally.`BLK Both firms are initially charging the same price, $200.00. Since per unit costs equal $100.00, the price exceeds per unit costs. A total of 600.00 units are demanded; each firm shares the quantity demanded equally, each firm sells 300.00 units. Click Firm A's up button in the $.01 Price Change row raising Firm A's price to $200.01. Firm B's price remains at $200.00. Since Firm B's price is now less, no one buys the good from Firm A and Firm A's profit drops from $30,000.00 to $0.00. `BLDSummary:`BLD Whenever both firms are charging the same price, a single firm will not raise the price unilaterally. ` Prob End ` Problem 1 Start Screen 2 - Bertrand Dynamics: Unilateral Price Decrease // 0: Title // Visibility sliders: Per unit cost, Demand constant, Demand price coefficient, // Price A, Price B L L L L L // 1: Label only, Both scrollbar and label // Initial values: Per unit cost, Demand constant, Demand price coefficient, // Price A, Price B 100 1000 -2 200 200 // 2: Initial values ` Text Start // 3: Text `RED`BLDObjective:`BLD Illustrate that whenever both firms are charging the same price that exceeds per unit costs, a single firm has an incentive to lower the price unilaterally.`BLK Again, both firms are initially charging the same price, $200.00. Since per unit costs equal $100.00, the price exceeds per unit costs. A total of 600.00 units are demanded; each firm shares the quantity demanded equally, each firm sells 300.00 units. Instead of clicking Firm A's up button in the $.01 Price Change row, click the its Down button. This lowers Firm A's price to $199.99. Firm B's prices remains at $200.00. Since Firm A's price is now less, no one buys the good from Firm B, Firm A attracts all the customers. `BLDQuestion:`BLD What happens to Firm A's profits? Does Firm A have an incentive to unilaterally lower the price by a small amount? `BLDSummary:`BLD Whenever both firms are charging the same price that exceeds per unit costs, a single firm has an incentive to lower the price unilaterally. ` Prob End ` Problem 2 Start Screen 3 - Bertrand Dynamics: Tit for Tat // 0: Title // Visibility sliders: Per unit cost, Demand constant, Demand price coefficient, // Price A, Price B L L L L L // 1: Label only, Both scrollbar and label // Initial values: Per unit cost, Demand constant, Demand price coefficient, // Price A, Price B 100 1000 -2 200 200 // 2: Initial values ` Text Start // 3: Text `RED`BLDObjective:`BLD Illustrate that whenever firms charge a price that exceeds per unit costs, each firm has an incentive to retaliate when the other reduces the price.`BLK Once again, both firms are initially charging the same price, $200.00. Since per unit costs equal $100.00, the price exceeds per unit costs. A total of 600.00 units are demanded; each firm shares the quantity demanded equally, each firm sells 300.00 units. Click Firm A's Down button in the $.01 Price Change row to reduce the Firm A's price by a small amount, $.01. As the previous screen illustrated, from A's profit rises dramatically. But now focus on Firm B. It has no customers; its profits have fallen to $0.00. Would Firm B just do nothing or would it retaliate? `BLDQuestion:`BLD Does Firm B have an incentive to respond by lowering its price by a small amount? Click Firm B's Down button to lower Firm B's price by $.01. The two firms now offer the same price and share the quantity demanded equally. Firm B is again earning positive profits, $29,998.00. `BLDQuestion:`BLD Does Firm B have an incentive to retaliate? However, perhaps Firm B can do even better than this. Suppose Firm B reduces its price by another small amount, by $.01. Click Firm B's Down button again. Firm B is now charging $199.98 while Firm A is still charging $199.99. Firm B now will attract all the customers and Firm A will be left with none. `BLDQuestion:`BLD Will Firm A now have an incentive to retaliate? Convince yourself that Firm A has an incentive to do so by reducing its price by $.02. `BLDQuestion:`BLD What is happening to the prices as each firm retaliates to the other? `BLDSummary:`BLD Whenever firms charge a price that exceeds per unit costs, each firm has an incentive to retaliate when the other reduces the price. Retaliation causes the prices to fall toward unit costs. ` Prob End ` Problem 3 Start Screen 4 - Bertrand Dynamics: An Equilibrium // 0: Title // Visibility sliders: Per unit cost, Demand constant, Demand price coefficient, // Price A, Price B L L L L L // 1: Label only, Both scrollbar and label // Initial values: Per unit cost, Demand constant, Demand price coefficient, // Price A, Price B 100 1000 -2 100 100 // 2: Initial values ` Text Start // 3: Text `RED`BLDObjective:`BLD Illustrate that a Nash equilibrium exists when both firms charge a price equal to per unit costs.`BLK Both firms now charge the same price, $100.00, just equal to per unit costs. Both firms now earn a profit of $0.00. `BLDQuestion:`BLD Will a firm have an incentive to rise its price by a small amount now? To answer this question click Firm A's Up button in the $.01 Price Change row to increase Firm A's price by a small amount, $,01, raising its price to $100.01. Firm A now has no customers; its profit does not rise, it continues to equals $0.00. `BLDQuestion:`BLD Will a firm have an incentive to reduce its price by a small amount now? To answer this question click Firm A's Down button in the $.01 Price Change row to reduce Firm A's price by a small amount, $,01, reducing its price to $99.99. Its price now falls short of per unit costs. Consequently, it incurs losses. `BLDSummary:`BLD When both firms charge a price equal to per unit costs, neither firm has an incentive to raise the price or lower the price. When both firms charge a price equal to per unit costs, a Nash equilibrium exists. ` Prob End """ }