a public good representing social order. Thus, government consumption is unproductive.
We take the good produced at each period t as the num´eraire.
2.1.1 Technology
The production technology is represented by a Cobb-Douglas production function,
F (Kt , Lt) = AKtαLt1-α , exhibiting constant returns to scale. This technology is the same
for all periods. At the end of each period the capital stock is completely depreciated.
We assume a representative firm producing at period t. The capital stock is owned by
the households who receive the profits of the firm. Since the production function is
homogenous of degree one, we can rewrite as:
f (kt) = Aktα, (1)
where A > 0 and α < 1 are technological parameters and k = K.
2.1.2 Households
Preferences The individuals live for two periods. When young, they work, receive a
wage and allocate this income between consumption and savings. When old they retire
and consume the return of their savings. These consumers also care about social order
which is preserved by institutions such as the police and the justice. The objective of the
households is to maximize their utility deriving from consumption and social order. The
young generation has to make two decisions: one about how much to save and one about
whether to overthrow the dictator.
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