ch02 - Microeconomic Theory Microeconomics: The branch of...

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1 Microeconomic Theory Microeconomics: • The branch of economics dealing with behavior of individual decision makers such as consumers and firms.
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2 Everyday Economics Wake up: Stay in bed Go to class Breakfast: Cereals and Juice Eggs, bacon and coffee Economics : Maximizing behavior
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3 Your trip to class You don’t have a car: Bus Cab You have a car. Have to stop for gas and prices are higher than last week: I don’t care about prices: full tank I’ll buy only half of what I bought last week I’ll take the bus Economics : Income effect Price elasticity
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4 On your way to class Need money: Bank loan Parent’s loan Money to invest: Buy some bonds Buy stocks online Economics : Price/cost is not only the money you have to pay: Psychological Cost Risk implicit in the good we buy
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5 On campus In class: Doze off Listen to the lecture After class: Economics 11 Biology Economics : Maximizing behavior Marginal rate of substitution Price/cost is not only the money you have to pay
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6 Chapter 2 THE MATHEMATICS OF OPTIMIZATION
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7 The Mathematics of Optimization • Why do we need to know the mathematics of optimization? • Consumers attempt to maximize their welfare/utility when making decisions. • Firms attempt to maximizing their profit when choosing inputs and outputs.
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8 Maximization of a Function of One Variable • The manager of a firm wishes to maximize profits: ) ( q f = f(q) Quantity * q* Maximum profits of * occur at q *
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9 Maximization of a Function of One Variable = f(q) Quantity * q* 1 q 1 0 q If the manager produces less than q*, profits can be increased by increasing q: – A change from q 1 to q* leads to a rise in
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10 Maximization of a Function of One Variable • If output is increased beyond q*, profit will decline – an increase from q * to q 3 leads to a drop in = f(q) Quantity * q* 0 q 3 q 3
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11 Derivatives • The derivative of = f(q) is the limit of  / q for very small changes in q h q f h q f dq df dq d h ) ( ) ( lim 0 • The value of this ratio depends on the value of q
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12 Value of a Derivative at a Point • The evaluation of the derivative at the point q = q 1 can be denoted 1 q q dq d • In our previous example, 0 1 q q dq d 0 3 q q dq d 0 * q q dq d
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13 Second-Order Derivatives • The derivative of a derivative is called a second-order derivative ' ' 2 2 ) / ( f dq f d dq dq df d
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This note was uploaded on 04/19/2010 for the course ECON Econ 11 taught by Professor Mcdevitt during the Spring '07 term at UCLA.

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ch02 - Microeconomic Theory Microeconomics: The branch of...

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