The Pontiac Assembly is a factory which uses labour and capital to build trucks according to the technology 1 1 f(L,K) =

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The Pontiac Assembly Is A Factory Which Uses Labour And Capital To Build Trucks According To The Technology 1 1 F L K 1 (39.49 KiB) Viewed 9 times

The Pontiac Assembly is a factory which uses labour and capital to build trucks according to the technology 1 1 f(L,K) = 415K₂ During a war, the government demands that the Pontiac Assembly produces 3 trucks for the military this year. The factory is currently renting 5 units of capital. Due to various limitations, the amount of capital the factory uses cannot be changed. The wage paid for each unit of labour is 8 and rent for each unit of capital is 4. Assume trucks, labour and capital are continuous variables. Represent labour in the horizontal axis and capital in the vertical axis. Answer the following: If rounding is needed, round your answers to 3 decimal places. a) Let Lo be the smallest amount of labour the factory must use to meet its production target. What is Lo? b) Suppose the factory employs L units of labour. What is the Marginal Product of Capital at this point? c) Suppose the factory employs I units of labour. What is the Technical Rate of Substitution MPL MPK -) at this point? d) After the war, the Pontiac Assembly sells trucks in a competitive market. The current market price for a truck is 100. The factory still cannot change the amount of capital it employs, but it controls the amount of labour it employs. How many trucks will the Pontiac Assembly produce to maximise profit? Note that the only decision variable this firm controls is the amount of labour it hires. Hint: express the profit function using the production function.

Lucy and Henry each have $6743. Each knows that with 0.1 probability, they will lose 85% of their wealth. They both have the option of buying a units of insurance, with each unit costing $0.1. Each unit of insurance pays out $1 in the event the loss occurs. The cost of the insurance policy is paid regardless of whether the loss is incurred. Lucy's utility is given by u¹(x) = x. Henry's utility is given by u¹(x) = √x. Answer the following: (If rounding is needed, only round at the end and write your answer to three decimal places.) a) Without insurance, what is the expected value of the loss? b) For Henry, facing the "lottery" above without any insurance is as bad as losing how many dollars for sure? c) Find Lucy's utility maximising choice of a. If more than 1 exist, enter the largest a. d) Now suppose insurance costs $0.2. Find Lucy's utility maximising choice of a. If more than 1 exist, enter the largest a. e) What is Henry's utility maximising choice of a with the new price of 0.2? If more than 1 exist, enter the largest a.