Demand and cost function faced by a firm is given as P = 12 - 0.4 Q an | Economics 0

Economics05 marksNumerical: profit maximization firmPrice and output determination under monopoly

Demand and cost function faced by a firm is given as P = 12 - 0.4 Q and $C = 5 + 4Q + 0.6Q^2$ . Find the equilibrium price, quantity, total revenue, total cost and total profit which maximizes profit of the firm. [5]

Demand and cost function faced by a firm is given as P = 12 - 0.4 Q and $C = 5 + 4Q + 0.6Q^2$. Find the equilibrium price, quantity, total revenue, total cost and total profit which maximizes profit of the firm. [5]

Demand function: $P = 12 - 0.4Q$ - Cost function: $C = 5 + 4Q + 0.6Q^2$ $TR = P \times Q = (12 - 0.4Q)Q = 12Q - 0.4Q^2$ $\pi = TR - C = (12Q - 0.4Q^2) - (5 + 4Q + 0.6Q^2)$ $\pi = 12Q - 0.4Q^2 - 5 - 4Q - 0.6Q^2 = -Q^2 + 8Q - 5$ $\frac{d\pi}{dQ} = -2Q + 8 = 0 \implies Q = 4 \text{ units}$ ...

Demand function: $P = 12 - 0.4Q$ - Cost function: $C = 5 + 4Q + 0.6Q^2$ $$TR = P \times Q = (12 - 0.4Q)Q = 12Q - 0.4Q^2$$ $$\pi = TR - C = (12Q - 0.4Q^2) - (5 + 4Q + 0.6Q^2)$$ $$\pi = 12Q - 0.4Q^2 - 5 - 4Q - 0.6Q^2 = -Q^2 + 8Q - 5$$ $$\frac{d\pi}{dQ} = -2Q + 8 = 0 \implies Q = 4 \text{ units}$$...

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Demand and cost function faced by a firm is given as P = 12 - 0.4 Q and C = 5 + 4Q + 0.6Q2. Find the equilibrium price, quantity, total revenue, total cost and total profit which maximizes profit of the firm.