If Firm B produces over 100 units after Firm A's 100-unit production, breaking the agreement, it could collect a maximum of $1 million (in millions) by selling the additional 100 units at $10 per unit.
Calculate the total revenue of the two firms if they produce 200 units.
the total revenue is:
Total revenue = $10/unit * 200 units = $2,000
Calculate the share of the total revenue that each firm would receive if they produce 100 units each.
Since the firms are splitting the production equally, each firm would receive half of the total revenue. Therefore, each firm would receive:
Share of total revenue = $2,000 / 2 = $1,000
Calculate the new price of the good if firm B produces more than 100 units.
To calculate the new price, we can use the formula for the equilibrium price:
Equilibrium price = (Total demand - Total supply) / (Coefficient of demand - Coefficient of supply)
In this case, the total demand is 200 units, the total supply is 100 units (from firm A) + Q units (from firm B), the coefficient of demand is -1, and the coefficient of supply is 1. Plugging these values into the formula, we get:
Equilibrium price = (200 - 100 - Q) / (-1 - 1) = -Q + 100
Setting the equilibrium price to $10, we get:
10 = -Q + 100
Solving for Q, we get:
Q = 90
Therefore, if firm B produces more than 100 units, the new price of the good would be:
New price = -Q + 100 = $-90 + 100 = $10
Calculate the new revenue of firm B if it produces more than 100 units.
the new revenue of firm B is:
New revenue = New price/unit * Quantity produced by firm B = $10/unit * Q units
Since firm B produces 90 units more than the equilibrium quantity, its total production is 100 units + 90 units = 190 units. Therefore, the new revenue of firm B is:
New revenue = $10/unit * 190 units = $1,900
Calculate the maximum dollar amount that firm B could collect if it breaks the production agreement and produces more than 100 units.
the maximum dollar amount that firm B could collect is:
Maximum dollar amount = New revenue - Share of total revenue = $1,900 - $1,000 = $900
he complete question:
Suppose firm A and firm B have agreed to produce a total of 200 units of a good. The equilibrium price for the good is $10 per unit. If firm A continues to honor the production agreement and produces 100 units, what is the maximum dollar amount (in millions) that firm B would collect if it breaks the production agreement and produces more than 100 units?