A single-owner firm faces a two-period planning problem with the transformation curve (1 + 4) 2 + 2 2 = 25 and initial resources equalling 1. Assume the market interest rate is 5%. Work out the firms initial wealth maximization problem and illustrate your answer in a diagram. [5 marks]

b) What happens if the market interest rate increases? When does the firm stop borrowing from the capital market in time 1? Explain, calculate, and illustrate your answer on top of the same diagram used in a). [5 marks]

c) Suppose the owner of this firm has the utility function of = 12 0.85 , with no other income or wealth. Using the same market interest rate of 5% and results from a), work out the utility maximisation problem and illustrate your answer on top of the same diagram [5 marks]