2. (40 marks) Suppose a firm uses the inputs labour (L) and capital (K) in the production of its output (Q), and the production function is Q = 2LK. The marginal products are MP;, = 2K and MPy = 2L. The wage rate (w) is $4, and the rental price of capital (r) is $4. Suppose the firm wants to produce 32 units of output. (1) What is the firm's optimal demand of labour and capital, if it wants to minimize its cost of production? What is the total cost of the firm's cost-minimizing choice of labour and capital? (2) Suppose the wage rate now changes to $1, what is the firm's cost-minimizing choice of labour and capital? How much does this combination cost? (3) Plot the isocost lines and isoquant curve for the firm's cost-minimizing choices in both (1) and (2) scenarios. Label the isocost lines with their equations and indicate the values of the x-intercept and y-intercept on the graph. Ensure that the vertical axis represents capital and the horizontal axis represents labour. (4) Use your answer in (1) and (2), graph the labour demand curve of this firm. Ensure that the vertical axis represents wage rate and the horizontal axis represents labour. (5) If the wage rate stays at $1 and rental price of capital stays at $4, but the firm wants to produce 72 units of output instead of 32 units, how many units of labour would the firm demand? Use your graph in (4) to show how this would change the firm's labour demand curve