Econ 407 Answers to Problems assigned on FRIDAY, Nov 12, 1999

PROBLEM 1 Evaluate the slope of each of the following functions at the points indicated.

a: at x=5, at x=3, c at x=4, d at x=6

> y:=5*exp(0.3*x);

> y1:=diff(y,x);

> eval(y,x=5);

> y:=4*exp(-2.4*x);

> y := 4*exp(-2.4*x);

Take first derivative as before and evaluate at x=4.

> y1:=diff(y,x);

> eval(y1,x=3);

> y:=ln(2*x^2+6*x+4);

y := ln(2*x^2+6*x+4)

> y1:=diff(y,x);

y1 := (4*x+6)/(2*x^2+6*x+4)

> eval(y,x=4.0);

4.094344562

> y:=ln(x+7);

y := ln(x+7)

> y1:=diff(y,x);

y1 := 1/(x+7)

> eval(y1,x=6);

1/13

>

Problem 2. You have been given the demand curve. Find the total Revenue by multiplying it by quantity. The demand

curve has been plotted for your convenience.

> p:=6.75*exp(-0.03*Q);

p := 6.75*exp(-.3e-1*Q)

Find total revenue function accorording to:

> TR:=p*Q;

TR := 6.75*exp(-.3e-1*Q)*Q

> plot(TR,Q=0..300);

Take the derivative of TR with respect to Q and set equal to zero. Solve for Q.

> MR:=diff(TR,Q);

MR := -.2025*exp(-.3e-1*Q)*Q+6.75*exp(-.3e-1*Q)

> solve(MR,Q);

33.33333333

Problem 3

Total Earnings = 8+2 = 10 see page 209 and 210.

0.10*8 +0.20 *2 = 1.2

>

> 0.10*8+0.20*2;

> 1.20/10;

Problem 4 see page 210 for a similar problem.

> .15*0.50 +0.05*.30 +0.04*.20;

Thus, the total growth in total revenue is 9.80 percent. Note that we multiply each revenue part by its respective rate of growth and sum over.

>

Assignment: Read Chapter 10: This is the introductory Chapter to Matrix Algebra!

>