Consider a corporation which has access to a production process which uses an input quantity
X to produce a quantity Y of a commodity, in no time. If production is going to happen, it will
happen at time t = 1. The factor price is constant, equal to unity, while the output price P(t)
at a future time t is stochastic. Assume that there is a forward market for the commodity, and
that there is a risk free interest rate.
In the following you are asked to explain how the corporation at t = 0 will value this
production possibility under different assumptions. It is not necessary to derive model results,
but you should make clear what assumptions are underlying the results you use.
In part (c) and (d), f is a strictly increasing, strictly concave production function.
(a)
The corporation can decide at t = 0 (but no later) to produce at t = 1. In case of
production, the magnitudes X and Y are exogenously given.
(b)
The corporation may wait until t = 1, when P(1) has become known, with deciding
whether to produce at t = 1. In case of production, the magnitudes X and Y are
exogenously given.
(c)
The corporation can decide at t = 0 (but no later) to produce at t = 1. Y will be equal
to f(X), and the magnitude X must be determined at t = 0.
(d)
Y will be equal to f(X), and the magnitude X must be determined at t = 0. But at t = 1,
when P(1) has become known, the corporation may decide to cancel production, and
in that case, it will not incur the cost X.
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