Market demand for the nuclear substance pluranium is given below, along with the TR for the given demand schedule. Pluranium is supplied to the world market by a monopolist. Suppose that the marginal cost of supplying an extra megatonne of pluranium is $20 and the business has FC=$60.

What is the profit-maximizing profit the monopolist will make?

Question

Market demand for the nuclear substance pluranium is given below, along with the TR for the given demand schedule. Pluranium is supplied to the world market by a monopolist. Suppose that the marginal cost of supplying an extra megatonne of pluranium is $20 and the business has FC=$60.

What is the profit-maximizing profit the monopolist will make?

BlackTom AI · Accepted Answer

The problem presents a monopolist facing a market demand table with corresponding total revenue (TR) and asks for the profit-maximizing profit given fixed costs (FC) and constant marginal cost (MC) of 20.

First, extract the marginal revenue (MR) for each additional unit sold by looking at the TR differences between successive quantities:
- From Q=0 to Q=1: MR1 = TR(1) − TR(0) = 70 − 0 = 70
- From Q=1 to Q=2: MR2 = TR(2) − TR(1) = 120 − 70 = 50
- From Q=2 to Q=3: MR3 = TR(3) − TR(2) = 150 − 120 = 30
- From Q=3 to Q=4: MR4 = TR(4) − TR(3) = 160 − 150 = 10
- From Q=4 to Q=5: MR5 = TR(5) − TR(4) = 150 − 160 = −10
- From Q=5 to Q=6: MR6 = TR(6) − TR(5) = 120 − 150 = −30
- From Q=6 to Q=7: MR7 = TR(7) − TR(6) = 70 − 120 = −50
- From Q=7 to Q=8: MR8 = TR(8) − TR(7) = 0 − 70 = −70

Second, compare MR with MC to find the profit-maximizing quantity. Since MC = 20, the monopolist will produce up to the highest quantity where MR is at least MC.
- MR1 = 70 > 20 (positive profit from selling the first unit)
- MR2 = 50 > 20
- MR3 = 30 > 20
- MR4 = 10 < 20
Thus, the profitable production stops at Q = 3 units, because the fourth unit would add only 10 to revenue, which is less than the cost of producing that unit (20).

Third, determine the price corresponding to Q = 3 from the demand schedule. At Q = 3, the price is P = $50.

Fourth, compute total cost (TC). With FC = 60 and MC = 20, the variable cost (VC) for Q = 3 is MC × Q = 20 × 3 = 60. Therefore, TC = FC + VC = 60 + 60 = 120.

Fifth, compute profit as TR − TC. TR at Q = 3 is 150, so profit = 150 − 120 = 30.

In summary, the monopolist maximizes profit by producing 3 megatonnes, selling at a price of $50, with a total cost of $120 and a total revenue of $150, yielding a profit of $30. Note: the provided single numeric answer field shows 60, which does not align with the calculated profit from the given TR schedule and costs.

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