6. [10 pts.] Firm X can choose between two technologies, A and B, to produce widgets.

Technology A will require the firm to pay $30,000 today and will allow the firm to produce UP TO 100,000 widgets one year from now at a variable cost of $1.50 per widget. (Suppose that the production of widgets occur, instantaneously, at t=1.)

Technology B will cost the firm $75,000 today and will allow the firm to produce UP TO 100,000 widgets at a variable cost of $1 per widget one year from now.

Suppose that the one-year forward price for widgets is $1.80 per widget. The price of a widget next year will be either $1.20 if the economy is bad or $2.20 if the economy is good.

Assume that rf =5% and that after producing the widgets at t = 1, both technologies become totally obsolete and you will cease all production.

a. Suppose that both technologies force the firm to produce 100,000 widgets one year from today. What is the firms value and which technology should Firm X choose?

b. [More challenging] Now suppose that the firm makes the technological choice at t = 0, pays the fixed cost today ($30k for Tech. A, or $75k for Tech B), but can wait until t = 1 to decide how many, if any, widgets to produce. What is the firms value and which technology should Firm X choose in this case?