Thompson Construction Ltd uses two main inputs (labour and capital) in its production process. The company is aiming to be a cost-minimizer therefore for any given output level the firm should be producing at the least possible cost. To achieve this objective the company must decide which technology is best for the firm. The company hires a consultant a to decide on which technology would be best to produce 1000 units of output given that the average price of labour and capital is $100 and $200 respectively. The consultant recommend the following production function Q = f (L,K) = 2L^1/3K^1/3

As a junior economist answer you are required to advise the directors of the company on how to minimize its cost of production

1. Derive the input demand function for the Cobb-Douglas production function.

(10 marks)

1. Determine the combination of labour and capital that the company should hire in order to maximize its output.

(4 marks)

1. What is the total cost at the optimal solution?

(2 marks)

1. Illustrate the firm's cost-minimization problem on a well labeled graph

(4 marks)