The accompanying table shows the demand schedule for vitamin D. Suppose that the marginal cost of producing vitamin \(\mathrm{D}\) is zero. $$ \begin{array}{c|c} \begin{array}{c} \text { Price of vitamin D } \\\ \text { (per ton) } \end{array} & \begin{array}{c} \text { Quantity of vitamin D demanded } \\\ \text { (tons) } \end{array} \\ \hline \$ 8 & 0 \\\ 7 & 10 \\\ 6 & 20 \\\ 5 & 30 \\\ 4 & 40 \\\ 3 & 50 \\\ 2 & 60 \\\ 1 & 70 \\ \hline \end{array} $$ a. Assume that BASF is the only producer of vitamin \(\mathrm{D}\) and acts as a monopolist. It currently produces 40 tons of vitamin \(\mathrm{D}\) at \(\$ 4\) per ton. If BASF were to produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect? Would BASF have an incentive to produce those 10 additional tons? b. Now assume that Roche enters the market by also producing vitamin \(\mathrm{D}\) and the market is now a duopoly. BASF and Roche agree to produce 40 tons of vitamin \(\mathrm{D}\) in total, 20 tons each. BASF cannot be punished for deviating from the agreement with Roche. If BASF, on its own, were to deviate from that agreement and produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect for BASF? Would BASF have an incentive to produce those 10 additional tons?

Step by step solution

01

a. Monopoly Price and Quantity Effects

Given that BASF is a monopolist and produces 40 tons of vitamin D at $4 per ton, we can first find the price effect and quantity effect if BASF were to increase the production by 10 tons. Price Effect: 1. Look at the demand schedule in the table provided. 2. Locate the price associated with the currently produced 40 tons, which is $4. 3. Locate the price associated with the new production level of 50 tons, which is $3. 4. Calculate the price difference: \(3 - \)4 = -$1. Thus, the price effect is -\(1 (i.e., a \)1 decrease in price per ton). Quantity Effect: 1. We are given that BASF produces 10 additional tons. 2. The quantity effect would be the increase in quantity demanded by 10 tons. Incentive to Produce Additional Tons: 1. Calculate the total revenue before the production increase: 40 tons * \(4 = \)160. 2. Calculate the total revenue after the production increase: 50 tons * \(3 = \)150. 3. Compare the two total revenues: \(150 < \)160. Since the marginal cost of producing vitamin D is zero and the total revenue decreases, BASF has no incentive to produce additional tons.

02

b. Duopoly Price and Quantity Effects

Now, we need to analyze the price and quantity effects of an increase in vitamin D production if the market becomes a duopoly with BASF and Roche. Price Effect: 1. The table remains the same as the market demand schedule doesn't change. 2. BASF and Roche agree to produce 40 tons together (i.e., 20 tons each) with a price of $4 per ton. 3. If BASF were to produce an additional 10 tons, they would now produce 30 tons. 4. Locate the price associated with the new market production of 50 tons, which is $3. 5. Calculate the price difference: \(3 - \)4 = -$1. Thus, the price effect in the duopoly scenario is also -\(1 (i.e. a \)1 decrease in price per ton). Quantity Effect for BASF: 1. BASF previously produced 20 tons. 2. BASF now produces 30 tons. 3. The quantity effect would be an increase of 10 tons. Incentive to Produce Additional Tons: 1. Calculate BASF's total revenue before the production increase: 20 tons * \(4 = \)80. 2. Calculate BASF's total revenue after the production increase: 30 tons * \(3 = \)90. 3. Compare the two total revenues: \(90 > \)80. Since the marginal cost of producing vitamin D is zero and the total revenue increases, BASF now has an incentive to produce additional tons when it deviates from the agreement with Roche.

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