2. (26 marks) A firm has the following production function: q = 2VKVL (a) (2 marks) Show the production function exhibits constant returns to scale. (Hint: Multiply K and L by 2 and show quantity produced is changed by 2.) (b) (2 marks) Show that the marginal product of any given quantity of capital in- creases as labour is increased. (Hint: Show what happens when L = 1 versus when L = 4.) (c) (2 marks) Set up the firm's problem. (d) (2 marks) Show that the value of the marginal product of labour = wage rate. (Hint: Use the firm's problem to show this.) (e) (6 marks) Suppose capital is fixed at K = 4, the wage w = $2, and price P = $18. Find the short run cost fuction C(q) = wL(q) + rK. Use the short run cost function to find q". (f) (2 marks) Find the value of r where the firm earns zero profits. g) (6 marks) Using the information at the start of this question, you can show the long run cost function for the firm is C(q) = 4 x Vur x q. Use w = 2 and the r from the previous section. (Note: If you can not find r in the previous question, use "fake = 128 for half marks here, but no additional penalty for the question.) What is the firm's problem? Do you need to know how many firms are in the market to find the supply curve here? What is the marginal cost curve? (h) (4 marks) If aggregate demand is P = 100 - -Q, what is the consumer surplus? What is the producer surplus? What is the dead weight loss? 'sSuppenine chillyiting mamboarmective market uses machines (K ) and workers (L) to produce containers of nails. Their production technology is given by 1= $12