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Question 1: Profit Maximization: Cobb-Douglas Technology Consider a firm that employs capital k and labour n and uses the production technology f(k,n) = kin. The price of output is p = 4, and the factor prices are r= 1 for capital and w=2 for labour. The amount of capital the firm uses in the current period is predetermined by past investment decisions, k = k= 4. a) Find the profit-maximizing input of labour n and the corresponding profit. b) Draw revenue and costs as a function of labour input in the same diagram. Identify the profit- maximizing level of n as well as the profit in your graph. c) Show the break-even levels of labour input in your graph, where the profits are exactly zero. Question 2: Profit Maximization: Leontief Technology Consider a firm that employs capital k and labour n and uses the production technology f(k,n) = min{k,n} (think of taxi cabs: you need exactly one car and one driver per taxi). The price of output is p = 4, and the factor prices are r= 1 for capital and w=2 for labour. The amount of capital the firm uses in the current period is predetermined by past investment decisions, k=k= 4. a) Find the profit-maximizing input of labour n and the corresponding profit. b) Draw revenue and costs as a function of labour input in the same diagram. Identify the profit- maximizing level of n as well as the profit in your graph. c) Show the break-even levels of labour input in your graph, where the profits are exactly zero

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