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ECON5026 Mid semester test, S2 2021

Solution Guide Part B (Sample Version)

PART B

Question 1

Suppose you have been investing in a bundle of selected stocks (Y). You are aware of your expected returns [E(Y)] and investment volatility measured by standard deviation () such that . For any given value of , explain your certainty equivalent and risk premium? (Use an appropriate fully labelled diagram in your answer). [6 Marks]

Answer Guide: 

Given   E(Y) = $1000 + $500 = $1500. The certainty equivalent is the amount that gives the same expected utility as the risky investment. Hence, the certainty equivalent is $1000.

The risk premium is the expected value less the certainty equivalent. That is, RP = E(Y) – CE = $1500 - $1000 = $500. This represents that you must be paid to make sure you are indifferent between the risky investment and the certainty equivalent.

The certainty index and the risk premiums are shown in the diagram below,

Question 2

Consider that a firm embarks on a month-long sales campaign with flexible pricing options for LED televisions and sound systems. There are four customers with valuations for each of these products as indicated in the table below:

The marginal and average cost of making a LED television is $900, and the marginal and average cost of making a sound system is $600.

Explain the optimal pricing strategy of the firm if:

(i) there is no budling

(ii) bundling of the two products

(iii)  a mix or optional bundling.

How much profit will the company make in each case?  (Show your work detail.)

            [7 Marks]

Answer Guide: 

The firm could consider alternative prising strategy based on non bundles, bundles and mixed bundles and then consider the strategy that gives it the maximum price. The various alternatives are explained in the following table:

No bundling

P_TV = P_SS = $500. In this case the firm sells TV and SS to everyone but makes a loss because the MC of TV =$900 and MC of SS = $600. So the firm makes a loss.

P_TV = P_SS = $1000. In this case the firm sells TV to Wang, John and Jessica and SS to John, Khan and Jessica. Profit = (6*1000 – (2700+1800)) =  $1500.

P_TV = P_SS = $1200 The firm sells TV to Wang and Jessica; and SS to Khan only. Profit = (3600 – 1800-600) = $1200.

Pure bundling – when the firm only offers a bundle

P_B =$1700 The firm sells the bundle to each customer. Profit = (4*1700 – 4*1500) = $800.

P_B =$2000 The firm sells only to John and Jessica. Profit = (2*2000 – 1500*2) = $1000.

(Also note that P_B=$2600 earns the firm profit = 2600 – 1500 = 1100.)

Mixed or optional bundling

The firm offers a bundle but also the items individually. Khan and Wang have valuations for TV and SS that are less than the relevant MC’s, respectively.

With a mixed bundling pricing strategy, the firm can sell the TV and SS to Wang and Khan individually and the bundle to John and Jessica. This is explained below.

If the firm charges P_TV =1300, P_SS =1200, P_B =2000 then the firm sells TV to Wang, SS to Khan and bundles to John and Jessica. Total profit = ($1300+$1200+2*$2000) – ($900+$600+$3000) = $6500 - $4500 = $2000. Hence this bundling strategy maximises profits for the firm.

Question  3

Explain the key differences between a Cournot and a Bertrand model of market structure. Draw the reaction functions for firms in a Cournot model and show market equilibrium output. How does the Cournot market output compare with output when the firms form a collusion and with output under competitive conditions?

Answer Guide:

The Cournot model originally developed by Augustine Cournot (1835) describes a specific case of oligopolistic market with engaged in quantity competitions. The firms produce identical products and hence they are forced to charge the same price. The firms have the only strategic choice on their outputs that they choose to produce, Q1 and Q2. Once the firms are committed to production, they set whatever price is necessary to clear the market. This is the price that consumers pay for the market output (Q1+Q2).

In Bertrand model (named after Joseph Bertrand in 1833)  is another type of oligopolistic market structure where firms are engaged in price competition. Each firm selects a price and stands ready to meet all the demand for its product at that price. In Bertrand's model, each firm selects a price to maximize its own profits, given the price that it believes the other firm will select.

In Cournot output competitions, reaction functions of any firm, say Alpha, shows Alpha’s profit maximising output for any level of output of the other firm (Beta).

The market equilibrium in a Cournot competitions is shown in the diagram below. The market equilibrium (Nash equilibrium) output are qa and qb, respectively.

When firms form a collusion, they act like a monopolist. The output under collusion is shown by point d and output under perfect competition is shown by point c. These entail lower and higher levels of firms’ output, respectively, compared to the Cournot output.