3. Assume that the production function for a certain production process is given by the following CobbDouglas production function: Q= L0.8 K0.4 (a) Derive expressions for the marginal products of L (labour) and K (capital), and hence find the marginal rate of technical substitution between L and K.

(b) If the wage rate is 10 and the cost of capital is also 10, what is the cost- minimising input bundle to produce 200 units of output? Illustrate this position on an isocost-isoquant diagram. If K is fixed in the short-run, what are the minimum costs in the short-run and long-run of increasing output to 300 units? Illustrate these positions on your diagram, showing the short-run and long-run expansion paths. Explain the cost differences.