An Algebraic Statement of the Shoven Model
Zero Net Profit
The unit cost of production in sector As is given by a
nested Leontief-CES function defined over the cost of intermediate inputs
and primary factors with ad-valorem taxes on factor demands. Unlike the
Harberger models, tax rates in this model are determined endogenously.
In equilibrium, the unit cost must be no less than the market price of
output:
and
Income Balance for Government
Government tax income (PT) is determined by the value of tax
revenue, calculated using activity levels, compensated demands,
market prices and ad-valorem tax rates:
Equal Yield
In equilibrium, tax rates are multiplicatively adjusted to achieve a target
level of government revenue:
Income Balance for Households
Household income is determined by the net of tax return to primary factors
plus the household share of government revenue:
Market Clearance for Goods
Producer output is equal to the sum of intermediate plus final demand:
where
is the household budget share devoted to the
consumption of goods, and eh is the "unit expenditure
function" which may be written:
Market Clearance for Factors
The aggregate supply of factors equals the sum of producer and
consumer demand. Producers pay taxes on factor inputs, consumers do
not because we consider these demands to be "leisure" or "household
production". Consumer demands for factors are specified as
Cobb-Douglas (constant budget shares):