Question 1 (a) Cyberdyne are making plans for production of the T-800 in 2020. They are confident that they will sell 180000 units and intend to produce that exact amount. Cyberdyne have a Cobb- Douglas technology which means that their production function is: f(x.x290107 where L and K are the inputs of labour and capital respectively. i. ii. iii. ii. iii. LUBS2410 Intermediate Microeconomics Seminar Questions 4 Find the marginal product of labour. Find the marginal product of capital. How does production change as Cyberdyne employ more labour? How does production change as Cyberdyne employ more capital? Sketch the production function with regard to labour and with regard to capital. (b) Cyberdyne can hire workers at a wage of 30 and rent machinery for 70. i. Use a Lagrangian to find how much labour and capital that Cyberdyne should employ. What is the minimum price that Cyberdyne would need to sell their production at to cover their total costs? Compute the technical rate of substitution. Sketch the isoquants. Derive the returns to scale. If Cyberdyne were confident that they could sell more than 180000 units at the same price, should they increase production? Use the Lagrangian multiplier to work out what would happen to costs if production increased by 50000. What would happen if production doubled? How does this result compare to the returns to scale that you computed in (aiii).