Public Finance, Foldvary

Anderson, Chapter 8: Government production and pricing of goods

Production versus provision

Example of production: education.

But contract out construction of schools.

Production function: equation, output as a function of inputs.

The function is technology and methods, including compliance with regulations.

q = f(k,l,n)

For schooling, output can be number graduated, scores on tests,

Total product, marginal product. Graphs p. 206.

In what region of output do profit-maximizing firms produce?

Where AP is falling and MP not negative.

Isoquant: p. 208. Curve of same quantity using various labor, capital goods.

Isoquant: a curve representing factors producing equal output.

Labor vertical, capital goods horizontal

Slope is the ratio of MP of labor, capital goods.

Marginal rate of technical substitution: MRTS or MRS: MPk/MPl

The rate at which one substitutes factors is the marginal rate of substitution,

MRS, the slope of the curve.

Because of diminishing marginal productivity, there is a diminishing rate of substitution

Curvature reflects substitutability; elasticity of substitution.

Perfect substitutes: straight line.

Perfect complements: angles.

Usually convex.

Optimal combination of inputs:

P. 211: Isocost curve

Isocost: a line showing combinations of inputs at the same total cost.

Given costs, production is maximized where the isoquant is tangent to the isocost.

MP/P are equal.

We want to mimimize the cost of producing a level of output q.

min(wL+rK such that y = f(L,K).

We take into account both production possibilities and costs.

The solution is a cost function c(L,K).

Suppose the inputs can be purchased at wage w and K cost c.

C = wL + rK, giving a combination of inputs with cost C.

Can draw isocost lines with axes L, K.

L = C/w -(r/w)K

Slope is -r/w, the negative of ratio of input prices.

The economic rate at which we can substitute inputs.

Isoquant for y=f(L,K) with lowest cost is tangent to the isocost curve (p. 212).

The MRTS equals the price ratio.

MPk/MPl = r/w

The marginal products of every dollar spent are equal.

Cost functions, p. 236.

Scale: the size of an operation (firm, factory).

Scope: types of output.

Economies of scale means that with a lager scale and mass production, the average product

increases. We get increasing returns to scale.

Diseconomies of scale means that average product decreases.

We get decreasing returns to scale.

When average total cost does not change with more output, this is a constant return to scale.

When average product increases, average cost decreases.

The long-run average cost curve tends to decrease and then increase.

It eventually can increase because of greater costs of management, coordination and overhead.

The antidote is to decentralize operations.

Economies of scope: lower average cost when combining various outputs.

Decreasing per-unit costs due to making several interdependent products.

Example: Integrate various police functions, rather than split into specialized units.

Combining on-site utilities may yield economies of scope (the heat from an

electricity generator could warm and distill water, for example).

Example: education

Many studies have examined the relationship between spending and student achievement.

The findings conclude that there is little relationship between size of classes and student performance.

There is no relationship between teachers’ education level and student achievement.

There is no relationship between teachers’ experience and student achievement.

No relationship between teachers’ salaries and educational output.

Expenditures per pupil have no effect on achievement.

What does account for student achievement?

Production of police protection

Safety services: protection from robbery, burglary, arson, assaults

No evidence of economies of scale.

There are economies of scope.

P. 220: pricing of public goods

Marginal cost pricing

P=MC the most efficient, if feasible.

Sometimes fairness trumps efficiency.

University: more costly for labs, music class, sports.

Two-part tariffs or pricing

Two charges: user fees, and fixed amount.

Charging MC plus fixed cost.

Two justifications for the type of tax.

Ability to pay; benefits principle.

User fees are for benefits receives.

Tolls are user fees.

Peak-load pricing.

Can apply to highways, electricity, mass transit, seasonal services.

Reduces the size of the operation.

Natural monopolies: decreasing average cost.

Increasing returns to scale.

Government ownership, or regulated monopoly.

Price discrimination.

Price discrimination: charging different prices to different buyers for the same type of good.

Examples: discounts to students, elderly.

Eastern Europe: foreigners pay more.

Perfect price discrimination: charge each buyer the maximum he or she would pay, squeezing out all consumer surplus.

Bigger monopoly profit with price discrimination.

No deadweight loss with perfect price discrimination