Consider the production function: F (L, K) = L^0.2K^0.7. The wage rate (price per unit of labour) is w = 2 and the capital rental rate (price per unit of capital) is r = 7. (a) Does this production function exhibit increasing, decreasing or constant returns to scale? Explain. What is the marginal productivity of labour and the marginal productivity of capital for (L, K) = (1, 1)? Would a firm (which minimises costs) use this combination of labour and capital? Explain. If your answer is yes, then what would be the quantity of production for which the company would use this combination? (b) Compute the quantity of labour and capital that this firm would use to produce y = 2 at the minimum cost. How much would this cost be? What is the average cost and the marginal cost for that production level? Hint: for this part, you can use directly (without providing the derivation) any results derived in the lecture or tutorials. (c) Derive the equation of the isoquant for y = 2 (with K in the vertical axis and L in the horizontal axis). Use the first and second derivative to show that this curve is decreasing and convex. Provide a graphical representation of the isoquant indicating at least one combination of labour and capital in this curve. (d) Suppose that instead the production function now is F (L, K) = 0.2L + 0.7K. The wage rate (price per unit of labour) is w = 3 and the capital rental rate (price per unit of capital) is r = 7. Obtain the cost function C(y), the marginal cost and the average cost. Derive the equation of the isoquant for y = 2 (with K in the vertical axis and L in the horizontal axis). Provide a graphical representation of this isoquant indicating the intersections with the vertical and horizontal axis.