dse micro

[econ14]

Consider a homogenous goods market with the demand
function q= 30-p  where Q and P denote quantity and price respectively.
There are two firms playing a price game in the following manner: firm1
quotes a price and then firm2 chooses a price. When they charge the same
price they share the market equally and otherwise the market demand goes
to the firm charging lower price. Firm 1 has a capacity constraint at the
output level 5 units such that upto five units the marginal cost of production
is Rs 3 per unit of output, however beyond 5 units it cannot produce any
output. Firm 2 does not have any capacity constraint, it can produce any
amount with the marginal cost Rs 6. What would be the equilibrium price
in the market?

a.  3
(b) 6
(c) 6- E ( E is small positive number)
d.  6+ E

[Prerna Rakheja]

Hi Sandeep,

There is typo in the question you have typed out, the option (d) is 3 + epsilon.
http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/2012-option-a.pdf

Answer:
(a) When price is 3, demand = 27. Firm 2 would not want to operate while Firm 1 can only produce upto 5 units so the market wont clear.

(b) When price is 6, demand = 24. Firm 1 would want to supply all 5 units as profit increases with each unit produced. Firm 2 is indifferent and hence would supply the remaining 19 units. Therefore, market clears.

(c) When price is 6 - epsilon, demand = 24 + epsilon. Firm 1 would want to supply all 5 units as profit increases with each unit produced. Firm 2 would not want to operate. Therefore, market wont clear.

(d) When price is 3 + epsilon, demand = 27 - epsilon. Firm 1 would want to supply all 5 units as profit increases with each unit produced. Firm 2 would not want to operate. Therefore, market wont clear.

So answer will be b