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Labour Supply And Neoclassical Production Function Notes

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Review Materials 11 October 2010

Topics

* Consumption and labour supply

* Neoclassical production function

* Profit maximization

* Competitive equilibrium and Pareto optimality

* Income tax and the Laffer curve

Reading

* Williamson (Chapter 4 and 5)

Key Points

* Consumer budget constraint

* Consumer optimization

* Effect of changes in real wages

* Income effect

* Substitution effect

Consumption of Labour Supply

* The representative consumer owns equal shares of firms in the economy

* We let be the after-tax non-wage income

* We assume that income tax is a lump-sum i.e. it is independent of the consumer's decisions Deriving the budget constraint

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*

* We combine them to give us:Consumer optimization

* There are two possible solutions when optimizing consumption between two goods (or baskets):

* Interior solutions (where the consumer chooses to consume both)

* Corner solutions (where the consumer chooses to consume just one goods basket) Indifference curves

* Indifference Curve = Curve that shows the combinations of consumption where the consumer is indifferent

* Slope of indifference curve is how willing the consumer is to forego consumption of good Y for good X

* The optimal consumption is when the budget constraint line touches the highest possible indifference curve
* Example of consumer optimization Changes in Real Wages

* To trace out the labour supply curve we have to look at the effects of an increase in real wages

* An increase in real wages has two effects: i. Income effect

* Since both leisure and consumption are normal goods, higher income implies that leisure and consumption both increase

* Substitution effect

* The price of leisure rises, so the consumer substitutes leisure for consumption

* If real wages increases, consumption must therefore rise, but leisure may rise or fall
* If the substitution effect > income effect, then the labour supply curve must be upward sloping
? Graph of the labour supply curve when income effect > substitution effect

* A shift in the labour supply curve occurs if real wage (after tax profits) increases Neoclassical Production Function

* The Production Function:
*is the total factor productivity (TFP)is the quantity of capital inputis quantity of labour input

* Production possibility frontier = Curve that determines the products you can produce

* Marginal rate of transformation (MRT) = slope of the production possibility frontier

* The neoclassical production function satisfies:

* Constant returns to scale
? Double all inputs, doubles output# For any

* Positive but diminishing marginal product of capital and labour

* Marginal Product = How much extra will be produced given a one unit increase in a factor of production (ceteris paribus)

* Ceteris paribus = All other things the same
? Marginal products are positive:
#
#
? Diminishing:
#
#

* Inada conditions

* Inada Conditions = An increase in workers eventually means that a machine becomes over utilised and useless

* MPK goes to infinity when K goes to zero

* MPK goes to zero when K goes to infinity

* Similar for MPN

* Together these properties allows us to plot the following aggregate production function
# Graph of aggregate production function

Profit Maximization

* Profits:
* i.e. Revenue - Wage Payment
* First order condition:

Course Notes Page 5

* Neoclassical production function

* Features of NPF (3)

* Profit maximization

* Competitive equilibrium

* Pareto optimality

* Welfare Theorems

* Laffer curve

* Effect of TFP | on Laffer curve and tax rate Definition

* Ceteris paribus = All other things the same

* First Welfare Theorem = Under certain conditions, a competitive equilibrium is Pareto optimal

* Inada Conditions = An increase in workers eventually means that a machine becomes over utilised and useless

* Indifference Curve = Curve that shows the combinations of consumption where the consumer is indifferent

* Laffer curve = Describes the relationship between total tax revenue and the tax rate

* Marginal Product = How much extra will be produced given a one unit increase in a factor of production (ceteris paribus)

* Marginal rate of transformation (MRT) = slope of the production possibility frontier

* Pareto Efficient = If the allocation of labour and consumption corresponds to the solution of a social planner, who maximises utility subject to the aggregate resource constraint of an economy

* Production possibility frontier = Curve that determines the products you can produce

* Second Welfare Theorem = Under certain conditions, a Pareto optimum is a competitive equilibrium Formula

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*

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* Pareto optimum:

* Tax revenue = tax rate x tax base

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