ECON7150 S1 2022
Assignment 2
Due June 3 2022 at 4 PM
Instructions:
All answers to the assignment must be neatly hand written.
Scan your assignment and save it as one pdf document. If you do not have access to a
flatbed scanner you can use a phone app such as “Adobe Scan” or “Microsoft Office Lens”.
Submit your assignment on Blackboard through Turnitin.
Make sure you show all steps, key formulae, and workings clearly. Final solutions should
be simplified as much as possible and either highlighted or circled. Round to the nearest
hundredth if necessary.
100 Marks – 30% of overall assessment
1. (18 marks) Suppose that there are two firms that are both producing the same good. Their
production levels are q1 and q2 respectively. If they produce at these levels, the price that
they will be able to charge is 100 6(q1 + q2). Each firm can produce at a marg
inal cost of 1
(their total costs are equal to the quantity that they produce).
a) (3 marks) Write down the profit maximization problem for firm 1, assuming that they take
the production levels of firm 2 as a given. In other words, write down firm 1’s problem as
if it were treating q2 as a constant.
b) (6 marks) Find the level of production q1 which solves the problem in part a) in terms of
q2. Be sure to show that this level of production satisfies both the first order and second
1
2order conditions. This is a single variable optimisation problem.
c) (6 marks) Complete the same exercise for firm 2, solving for the optimal level q2 that
maximises profits for firm 2 while treating q1 as a constant. This is a single variable
optimisation problem.
d) (3 marks) Find the levels of q1 and q2 which satisfy the conditions you found in parts b)
and c).
2. (16 marks) Define A =