Jack is the manager at a bottling company with a production function of

Q = K^0.3L^0.9

The bottling company pays its employees $12.50 per hour and is charged $250 per unit on the machinery it rents.

a. Assuming Jack has a budget of $800,000, what are the amounts of capital and labour he should employ in order to minimize costs?

b. What output can Jack produce with this budget? Show your results on a graph.

c. If the wage rate rises to $20, and Jack wants to produce the same output as before, what amounts of labour and capital will he need? Find the corresponding budget.

d. If Jack had the same budget as in part a) how much labour and capital should he use with the new wage rate? What would the output be?

e. Calculate the effect on labour employment from the substitution and scale effect. Show all results on a graph.