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Lecture6

# Lecture6 - Lecture Conclusion of Nonlinear Break-Even...

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Lecture 1/28/08 Conclusion of Nonlinear Break-Even Example Time Value of Money a. Future Value of an investment b. Present Value c. Future Value of a Sequence of Deposits

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Break-Even Points Plots of Total Costs and Revenue -\$500.00 \$0.00 \$500.00 \$1,000.00 \$1,500.00 \$2,000.00 \$2,500.00 \$3,000.00 \$3,500.00 0 20 40 60 80 100 Production Quantity Costs and Revenues Total Profit Total Cost Revenues Break – Even Points
Minimum Average Cost Marginal and Average Costs and Revenues \$20.00 \$25.00 \$30.00 \$35.00 \$40.00 20 40 60 80 100 Production Quantiy Costs and Revenues Average Cost Marginal Cost Marginal Revenue Average Cost is a minimum at Q where Marginal cost=Average Cost

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Non-linear Total Cost Example (c) Find weekly production level Q* that minimizes the average cost A(Q) A(Q)=TC(Q)/Q=( 250+20Q+.10Q 2 )/Q A(Q)=250/Q + 20 + .10Q If Q* minimizes A(Q) then A´(Q*)=0 A´(Q*)=-250/(Q*) 2 +.10 =0 (Q*) 2 = 2500 => Q*=50 Marginal and average costs are equal at Q*=50
Time Value of Money Notation . A= Investment amount at the start of a time period(\$) p= Periodic interest rate expressed as a decimal FV=Future value of an investment, value at the end of a time period.

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