17  Advertising

For more information on these topics, see Allen, Doherty, Weigelt, and Mansfield Chapter 8: Monopoly and Monopolistic Competition.

17.1 Practice Questions

First, here are some practice questions on the Classwork 16 material.

Question 1: A monopolist chooses its output based on:

Price equals Marginal Cost
Price equals Average Cost
Marginal Revenue equals Marginal Cost
Price equals Marginal Revenue

Question 2: For a linear demand curve P = a - bQ, the Marginal Revenue (MR) curve is:

MR = a - bQ
MR = a - 2bQ
MR = 2a - bQ
MR = 2a - 2bQ

Question 3: Compared to perfect competition, a monopolist typically:

Charges lower prices and produces more output
Charges higher prices and produces less output
Charges the same prices and produces the same output
Charges lower prices and produces less output

Question 4: If the price elasticity of demand is -2, what happens to total revenue when price increases?

Total revenue increases
Total revenue decreases
Total revenue remains unchanged
It’s impossible to determine without more information

Question 5: On which part of the demand curve will a profit-maximizing monopolist always operate?

The inelastic portion
The elastic portion
The unit elastic point
It depends on the specific demand curve

17.2 Classwork 17: Advertising

Monopolistic Competition

Many real-world industries fall between perfect competition and monopoly. In monopolistic competition:

• Many firms compete, selling similar but differentiated products.
• Firms can gain some market power through branding and advertising.
• There are low barriers to entry.
• In the short run, firms may earn profits.
• In the long run, new entrants drive economic profits to zero.

This market structure explains industries like restaurants, clothing brands, and many consumer goods, where companies compete on both price and product features.

1. A simple model of advertising’s impact on demand: Suppose a firm faces the demand curve \(P = 50 - 0.5 Q + 2.5 \sqrt{A}\), where \(A\) is the firm’s advertising expenditure.

   1. Draw a ggplot using stat_function to visualize the effect of increased advertising expenditure on on demand. Assume \(P\) is fixed at $30 per unit, and draw \(A\) on the x-axis against \(Q\) on the y-axis. Interpret your visualization.

   2. Recall that the price elasticity of demand is given by \(\varepsilon = \frac{% \Delta Q}{% \Delta P} = \frac{dQ/Q}{dP/P}\). Show that for this demand function, \(\varepsilon = \frac{-2P}{100 - 2P + 5 \sqrt{A}}\).

   3. Interpret the elasticity: as advertising expenditure \(A\) increases, do consumers find it easier or harder to escape the market when prices increase (that is, when A increases, does demand become more elastic or less elastic)?

2. Solve for the optimal advertising expenditure: Suppose a firm faces demand given by \(P = 100 - Q + \sqrt{A}\), and their total costs are given by \(TC = 10Q + A\). Find the firm’s optimal advertising expenditure A by using the MR = MC rule: the MR of increasing quantity should be equal to the MC of increasing quantity, and the MR of increasing advertising expenditure is equal to the MC of increasing advertising expenditure.

   1. Let \(TR = PQ\) and find the marginal revenue of increasing Q: \(\frac{\partial TR}{\partial Q}\).

   2. Find the marginal revenue of increasing \(A\): \(\frac{\partial TR}{\partial A}\).

   3. Find the marginal cost of increasing \(Q\): \(\frac{\partial TC}{\partial Q}\).

   4. Find the marginal cost of increasing \(A\): \(\frac{\partial TC}{\partial A}\).

   5. Setting \(MR_Q = MC_Q\) and \(MR_A = MC_A\) gives you two equations and two unknowns. Solve them: you should find that \(A = 900\) and \(Q = 60\). What is the rationale behind setting MR = MC in both of these dimensions to find optimal choices?