1.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)

2.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 =K^1/3L^1/3M^1/3. 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)

3.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)

4.Jabil owns two production plants and make microchips. The plants produce identical products, and each plant has a production function as for 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)

5.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)