Question

1. Suppose the firm is a monopolist. It faces a downward-sloping demand curve, P(Q). If it also has non-negative marginal cost, will it choose a quantity on the demand curve where the price elasticity of demand is less than, greater than, or equal to -1? Explain.

Two Hints: First, recall that R(Q) = P(Q) times Q, and that the price elasticity of demand is defined as .

Second, recall the condition MR = MC. Think about how the firm’s revenue will change if it starts at a point where the price elasticity is exactly -1 and increases Q by 1%, and remember that any increases in Q has a marginal cost.  

Answer 1

A monopoly competition is where there is only one seller and huge number of buyers due to which there remains no competition for the seller and no substitutes for the buyers. Therefore, a monopolist has ultimate control over the price of the commodity which is known as monopoly power of the firm. under this market, the firm can earn super normal profits but then also the firm has to keep its price low in order to sell more quantity in the market due to which they have a downward sloping demand curve.

Because the monopolist is the market's only supplier, the demand curve the monopolist faces is the market demand curve. The fact that the monopolist faces a downward‐sloping demand curve implies that the price a monopolist can expect to receive for its output will not remain constant as the monopolist increases its output.

Because a monopoly firm has its market all to itself, it faces the market demand curve. Figure -1 compares the demand situations faced by a monopoly and a perfectly competitive firm. In this figure the equilibrium price for a perfectly competitive firm is determined by the intersection of the demand and supply curves. The market supply curve is found simply by summing the supply curves of individual firms. Those, in turn, consist of the portions of marginal cost curves that lie above the average variable cost curves. Hence the break in the horizontal axis indicating that the quantity produced by a single firm is a trivially small fraction of the whole. In the perfectly competitive model, one firm has no relation with the determination of the market price. Each firm in a perfectly competitive industry faces a horizontal demand curve defined by the market price.

Figure-1

Figure-2

Therefore, the situation shown in Figure -1 with the one faced by the monopoly firm in Figure-2, since it is the only supplier in the industry, the monopolist faces the downward-sloping market demand curve alone and it may choose to produce any quantity. However, in the perfectly competitive firm, which can sell all it wants at the going market price, a monopolist can sell a greater quantity only by cutting its price.

Suppose, for example, that a monopoly firm can sell quantity Q1 units at a price P1 as shown in Figure-2. So, if it wants to increase its output to Q2 units and sell that quantity, it must reduce its price to P2. To sell quantity Q3 it would have to reduce the price to P3. The monopoly firm may choose its price and output, but it is restricted to a combination of price and output that lies on the demand curve. Hence it cannot charge price P1 and sell quantity Q3. To be a price setter, a firm must face a downward-sloping demand curve.

A firm’s elasticity of demand with respect to price has important implications for assessing the impact of a price change on total revenue, also, the price elasticity of demand can be different at different points on a firm’s demand curve. We can see why a monopoly firm will always select a price in the elastic region of its demand curve.

Suppose the demand curve facing a monopoly firm is given by equation where Q is the quantity demanded per unit of time and P is the price per unit:

Equation –

Q=10−P

This demand equation implies the demand schedule as shown in Figure for “Demand, Elasticity, and Total Revenue”. The total revenue for each quantity equals the quantity times the price at which that quantity is demanded. The monopoly firm’s total revenue curve is given in Figure-3, because a monopolist must cut the price of every unit in order to increase sales, total revenue does not always increase as output rises. Here the total revenue reaches a maximum of $25 when 5 units are sold and beyond 5 units, total revenue begins to decline.

Henceforth in the perfectly competitive case, the additional revenue a firm gain from selling an additional unit and its marginal revenue is equal to the market price. The firm’s demand curve, which is a horizontal line at the market price, is also its marginal revenue curve but a monopoly firm can sell an additional unit only by lowering the price.

Since as there is a relationship between the firm’s demand curve and the price elasticity of demand, there is a relationship between its marginal revenue curve and elasticity. Where marginal revenue is positive, demand is price elastic. Where marginal revenue is negative, demand is price inelastic. Where marginal revenue is zero, demand is unit price elastic.