Economics20785 marksNumerical: profit maximization firmPrice and output determination under monopoly
Let the demand and cost functions are P = 12 - 0.4Q and C = 5 + 4Q + 0.6Q² respectively. Then find the equilibrium price, quantity, total revenue, total cost and total profit.
Let the demand and cost functions are P = 12 - 0.4Q and C = 5 + 4Q + 0.6Q² respectively. Then find the equilibrium price, quantity, total revenue, total cost and total profit. [5]
- Demand function: $P = 12 - 0.4Q$ - Cost function: $C = 5 + 4Q + 0.6Q^2$ $$TR = P \cdot Q = (12 - 0.4Q)Q = 12Q - 0.4Q^2$$ $$MR = \frac{d(TR)}{dQ} = 12 - 0.8Q$$ $$MC = \frac{dC}{dQ} = 4 + 1.2Q$$ Set $MR = MC$: $$12 - 0.8Q = 4 + 1.2Q$$ $$8 = 2Q \implies Q = 4 \text{ units}$$ Second-order check: