Question

Need a detailed explanations for question 4.

1. Suppose there are two firms, Boors and Cudweiser, each selling identical-tasting nonalcoholic beer. Consumers of this beer have no brand loyalty so market demand can be expressed as P = 5 − .001(QB + QC). Boors’ marginal revenue function can be written MR = 5 − .001(2QB + QC) and symmetrically for Cudweiser. Boors operates with out-of-date technology and has constant cost of $2 per unit , whereas Cudweiser has constant cost of $1 per unit. Assuming the firms behave as Cournot competitors, Boor’s best-response function is

a. QB = 2,000 − .5QC b. QB = 1,500 − .5QC c. QC = 2,000 − .5QB d. QC = 1,500 − .5QB

2. Consider the same market for nonalcoholic beer as in the previous question. Cudweiser’s response function is a. QB = 2,000 − .5QC b. QB = 1,500 − .5QC c. QC = 2,000 − .5QB d. QC = 1,500 − .5QB

3. Consider the same market for nonalcoholic beer as in the previous question. How many “units” of beer will Boors produce in the Nash equilibrium? a. 667 b. 1,667 c. 2,333 d. 3,000

4. Consider the same market for nonalcoholic beer as in the previous question. How many “units” of beer will Cudweiser produce? a. 667 b. 1,667 c. 2,333 d. 3,000

Answer 1

(4) (b)

For Boors,

TR = P x QB = 5QB - 0.001QB² - 0.001QBQC

MR = TR/QB = 5 - 0.002QB - 0.001QC

Equating MR = MC,

5 - 0.002QB - 0.001QC = 2

0.002QB + 0.001QC = 3

2QB + QC = 3,000

2QB = 3,000 - QC

QB = 1,500 - 0.5QC (1) (Best response)

For Cudweiser,

TR = P x QC = 5QC - 0.001QBQC - 0.001QC²

MR = TR/QC = 5 - 0.001QB - 0.002QC

Equating MR = MC,

5 - 0.001QB - 0.002QC = 1

0.001QB + 0.002QC = 4

QB + 2QC = 4,000

2QC = 4,000 - QB

QC = 2,000 - 0.5QB (2) (Best response)

Substituting (2) into (1),

QB = 1,500 - [0.5 x (2,000 - 0.5QB)] = 1,500 - (1,000 - 0.25QB) = 1,500 - 1,000 + 0.25QB = 500 + 0.25QB

0.75QB = 500

QB = 667

QC = 2,000 - (0.5 x 667) = 2,000 - 333 = 1,667