John company has the production function Q = LK. The company initially faces input prices w = 1 and r = 1, and plans to produce Q = 100. One year later the price of labour (w) increases by 3. Calculate the company's price elasticity of demand for labour over this range of prices.

(4 marks)

A firm needs to use three types of inputs to produce its output: capital (K), labour (L) and materials (M). The firm's production function is given by Q =K1/3L1/3M1/3. The prices of capital, labour, and materials are r = 1, w = 1, and m = 1, respectively. When Q = 4, the long-run cost-minimizing quantity of capital is 4. If capital is fixed at 4 in the short run, show that the short-run and long-run cost-minimizing quantities of labour and materials are the same.

(4 marks)

The production of Lim company is given by Q = KL + M. The prices of input of K, L and M are 4, 16, and 1, respectively. The company is operating in the short run, with K fixed at 20 units. What is the short-run total cost of producing 400 units of output?

(4 marks)

Jabil owns two production plants and make microchips. The plants produce identical products, and each plant has a production function asfor i = 1,2. Specifically, plant 1 has K1 = 25, whereas plant 2 has K2 = 100. Input prices for K and L are w = r = 1. When output is optimally allocated between the two plants, calculate the firm's short-run total, average, and marginal cost curves.

(4 marks)

An airline company has a production function of two inputs, labour and capital, given by . Let w = 2 and r = 1. Find the equation of the company's long-run total and average costs.

(4 marks)