Final answer:
The social welfare cost in a monopolistic market can be calculated by subtracting the monopolist's total cost from the total revenue. This can be found by substituting the revenue and cost functions into the equations and calculating the difference.
Step-by-step explanation:
The social welfare cost in this monopolistic market can be calculated by subtracting the monopolist's total cost from the total revenue. The monopolist's total cost function is given as CT(q) = 6q^2, and the reverse demand function is p = 643 - 2q. To find the monopolist's total revenue, we need to multiply the price (p) by the quantity (q) sold. Substituting the reverse demand equation into the total revenue equation, we get:
Total Revenue (TR) = p * q = (643 - 2q)q
Next, we can find the monopolist's total cost by substituting the cost function into the equation:
Total Cost (TC) = CT(q) = 6q^2
The social welfare cost is then equal to total revenue minus total cost:
Social Welfare Cost = TR - TC = (643 - 2q)q - 6q^2
Social welfare cost, in the context of a monopolistic market, refers to the deadweight loss caused by not achieving the economically efficient equilibrium output of a perfectly competitive market.
The student asks about the social welfare cost in a monopolistic market. Social welfare cost in the context of a monopolist can be referred to as the deadweight loss, which is the loss of economic efficiency when the equilibrium outcome is not achievable or not achieved. In the monopoly scenario described, the monopolist would produce at the quantity where marginal revenue (MR) is equal to marginal cost (MC). To determine this quantity, we set the MR, which is the derivative of the total revenue (TR = price (P) * quantity (Q)), equal to MC and solve for the quantity. The deadweight loss, which represents the social welfare cost, would be the area between the demand curve and the marginal cost curve from the monopoly quantity to the quantity that would have been produced in a perfectly competitive market.