Question

LUBS2410 Intermediate Microeconomics Seminar Questions 4 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: fxi, 0 where L and K are the inputs of labour and capital respectively i. 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. ii. Compute the technical rate of substitution. Sketch the isoquants. ii. 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? (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. ii. What is the minimum price that Cyberdyne would need to sell their production at to cover their total costs? ii. Use the Lagrangian multiplier to work out what would happen increased by 50000. What would happen if production doubled? How does this result compare to the returns to scale that you computed in (aii).

Answer 1