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Mathe III Lecture 2 Mathe III Lecture 2

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2 _____________________________________ Montag 8.00 – 9.30 Uhr – HS H Montag Uhr – HS H Mittwoch 8.00 – 9.30 Uhr – HS M Mittwoch 9.30 – Uhr – HS M Tutorien im WS 2004/05 Mathe III Chong-Dae KIM

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3 The Cobweb Model

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4 Cost of raising q pigs: : Demand for pigs: N (profit maximizing) farms producing pigs Each farm, takes p as given and maximizes: It takes one period to raise a pig

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5 Supply: Farmers decide at t-1 on the production at t

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6 The Stationary State p* :

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7 Graphic illustration:

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8 etc. etc

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11 a reminder Savings Equation: Its solution:

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12 a 2 nd reminder First order equation with constant coefficient Its solution:

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13 Etc. After 1 period

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14 After t periods is the Present Value of

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16 The present values of the streams of consumption and income are equal The present values of the streams of consumption and income are equal

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17 Mortgage Repayments Outstanding Balance At time t Repayment per period

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18 Mortgage Repayments

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19 The loan equals the present value of T payments of z

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20 We found that: and:

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21 For t-1 this becomes: Interest on last period’s principal Payment towards the principal

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22 Payment towards the principal For t=1: For t=T: Interest: principal repayment: Interest: principal repayment: small large small large

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23 Linear Equations with a Variable Coefficient

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24 Linear Equations with a Variable Coefficient

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25 example The solution to: is: or:

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26 The general solution becomes:

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27 then: ( the present value, at t = 0, of $1 at t )

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29 or: the present value at period 0 the present value at period t

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30 Second Order Equations etc.

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31 Existence and Uniqueness : The equation has a unique solution for any given

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