1. Multi-Product Monopolist - Learning By Doing

Firms that produce plane engines are known to have cost functions that
exhibit learning-by-doing. Consider the following problem. Suppose that
there is only one firm that produces engines and that this firm chooses its
production level for t = 1 and t = 2. Suppose that the interest rate is equal
to 0 and the cost functions are equal to C1(q1) = (1/2)*q1 and C2(q2, q1) = 1/2*q2*(1−q1). 
The demand functions are D(p1) = 1−p1 and D2(p2) = 1−p2,respectively.
(a) Determine whether the firm’s costs exhibit learning-by-doing.
(b) Write down the problem of the firm and determine the optimal quan-
tities q1 and q2.
(c) Compute the prices and profits.
(d) Suppose that the cost function for t = 2 is C2(q2) = 1
2 q2. Answer all
questions above and compare your answers.
(e) Is this problem an example of learning by doing? Discuss.