Sample Mathematics Problems Economics 41

These problems are provided to you so that you can check whether you are familiar with the material on the mathematics review sheet, handed out in class. You should read that sheet first, then attempt these problems. If you can do them all after reading the sheet, then you should have no problem with the mathematics used in the class. If these problems are not clear after reading the sheet, then you are welcome to visit me in office hours and I will go over whatever material you would like me to go over until you are comfortable with it.
Answers to the sample problems will be handed out on Wednesday, and will be available on the web at that time.

1. Graph the function y = 20-2x. What is the slope of this line?

2. Find the derivatives of the following four functions:
a) y = 1/4*x²
b) y = 4
c) y = 20-2x
d) y = 3*x^4/3

3. Graph the function p = 5 + 2q₁ -q₂ for the case when q₁=1. Then, on the same graph, graph it when q₁=3. Does an increase in q₁ cause the graph to rise or fall?

4. If p = 5 + 2q₁ - q₂², find the partial derivatives ¶p/¶q₁ and ¶p/¶q₂.

5. In the following graph, find an approximate value for P when Q=7.

6. Graph the function y=x³. What is the slope of this function at the point x=2? Using this slope, find an approximate value for y when x=2.1. Then use a calculator (or a pencil) to find 3.1³. How close is your approximation?

7. The supply of cucumbers is given by Q = 5 + P. The demand for cucumbers is given by Q = 17 - 2P. Find the equilibrium quantity of cucumbers and the equilibrium price.