ECON 6313-001

Fall semester, 2013

Professor C. Brown

Homework Assignment #2

Please submit the following problems on Wednesday, September 18. This assignment is worth 10 points.

1.  This question is based on Figure 1.

a.  Assuming the location given by point X is one mile east of Town C. Compute total travel miles (TTM) to a football stadium located at point X.

b.  Compute the change in total travel miles (DTTM) by moving the stadium location to 1 mile east of point X.

c.  Assuming the objective is to minimize TTM, what is the optimal location for the Stadium?

2.  Fill in the blanks in the following table. Then use the table to answer the questions:

X / Total
Benefit / Total
Cost / Marginal
Benefit / Marginal
Cost / Net
Benefit
0
1
2
3
4
5
6 / _____
200
_____
_____
450
_____
500 / 0
30
_____
_____
_____
255
_____ / xx
_____
100
_____
_____
30
_____ / xx
_____
_____
50
65
_____
75 / 0
_____
230
270
_____
_____
_____

a.  If activity X is increased from 3 to 4 units, total benefit ______by $______.

b.  .If X is increased from 3 to 4 units, total cost ______by $______.

c.  If X is decreased from 6 to 5 units, total benefit ______by $______, and total cost ______by $______. Thus, net benefit ______.

d.  The optimal level of activity is ___ units of activity X, and net benefit at the optimal level of X is $______.

3.  A cocoa shipping firm has determined that its U.S. demand curve is given by:
Q = 7,500 – 3P
where Q is metric tons of cocoa and P is the price per metric ton. The firm can import cocoa from the Ivory Coast for $1,850 per metric ton. Its shipping cost is $104 per metric ton of cocoa. The company has fixed costs of $2,000.

e.  Write the inverse demand function and illustrate with a simple diagram

f.  Write the revenue function. At what level of output (Q) is revenue maximized?

g.  Display the profit function.

h.  Indicate the level of profit (or losses) if Q = 0

i.  Determine the optimal price and quantity for this firm.

j.  Suppose the U.S. government imposed an import tariff of $270 per metric ton of cocoa. Compute the effect of the tariff on the optimal price and quantity sold by this firm. Does the tariff affect profits? Explain.

4.  Find dy/dx for the following functions:

a.  y =

b.  y =

c.  y =

d.  y =

e.  y =

f.  y =

1