If the monopolist firm of Exercise 3, was a public sector firm. The government set a rule for its manager to accept the goverment fixed price as given (i.e. to be a price taker and therefore behave as a firm in a perfectly competitive market), and the government decide to set the

Question

If the monopolist firm of Exercise 3, was a public sector firm. The government set a rule for its manager to accept the goverment fixed price as given (i.e. to be a price taker and therefore behave as a firm in a perfectly competitive market), and the government decide to set the price so that demand and supply in the market are equal. What would be the equilibrium price, quantity and profit in this case?

Accepted Answer

> [!TLDR]
> As a price taker the manager sets $P = MC = 0$ (all cost is fixed); demand $P = 110 - 10q$ then gives $q = 11$, and profit $= 0 - 100 = -	ext{Rs }100$.

> [!NOTE]
> **A note on the cross-reference.** The exercise refers to 'the monopolist firm of Exercise 3', but Exercise 3 is a short conceptual question, not a firm with a demand and cost schedule. The firm actually intended is the **monopoly firm with total fixed cost Rs 100** of the previous numerical exercise. We solve it on that basis and flag the reference honestly rather than guess a different firm.

That firm has **only a fixed cost** of Rs 100, so its **marginal cost is zero**. When the manager is told to behave as a **price taker**, the competitive equilibrium condition is **price = marginal cost**, so the government would set **price = Rs 0**.

The demand schedule ($q = 1$ at $P = 100$, $q = 2$ at $P = 90$, …) is the straight line $P = 110 - 10q$. Setting $P = 0$ gives

$$0 = 110 - 10q \;\Rightarrow\; q = 11.$$ …

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