5.8 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 (it is not costly to start a business).
  • 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: 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.

Answer: \[\begin{align} \end{align}\]

library(tidyverse)

As your advertising expenditure increases, people demand more of your good, but the effect has diminishing marginal benefits.

  1. The price elasticity of demand is given by \(\varepsilon = \frac{\% \Delta Q}{\% \Delta P} = \frac{dQ/Q}{dP/P}\). That is, you can calculate the demand elasticity by finding the partial derivative of Q with respect to P, and then multiplying it by P/Q. Show that for this demand function, \(\varepsilon = \frac{-2P}{100 - 2P + 5 \sqrt{A}}\).

Answer: \[\begin{align} \end{align}\]

  1. 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)?

Answer:

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 marginal revenue = marginal cost 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: \(\frac{\partial TR}{\partial Q}\).

Answer: \[\begin{align} \end{align}\]

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

Answer: \[\begin{align} \end{align}\]

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

Answer: \[\begin{align} \end{align}\]

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

Answer: \[\begin{align} \end{align}\]

  1. 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?

Answer: \[\begin{align} \end{align}\]