Q1 [10 marks]. A small high-tech company has the following production function: Q=0.2lnL+0.4an+0.4lnH, where K represents special equipment, L is low-skilled labour and H is high-skilled labour. The market price of one unit of equipment is 2, the wage of a low- skilled worker is 1, and the wage of a high-skilled worker is 4. The company seeks to maximise its output. However, their budget is limited to 100. There are only 12 high-skilled workers looking for a job, and only 25 units of required equipment are available on the market. a) Write down the constraints the company faces. [2 marks] b) Write down the Lagrangian under the assumption that all of the constraints are binding. [2 marks] c) Derive the first-order conditions for the Lagrangian you wrote in part b). Explain why the equipment and high-skilled labour constraints are slack. (Hint: What are the values of the Lagrange multipliers associated with the equipment and high-skilled labour constraints?) [3 marks] d) Find the optimal combination of L, K and H. (Hint: from part c, you know that only the budget constraint is binding.) [3 marks]