Managerial Economics (ECON 3305)

Please solve all of them!!!

1)If core price inflation has grown at a compound growth rate of 2 percent per annum in the United States and 0.06 percent in Japan for the past ten years, what exchange rate represents PPP today if the two currencies ten years ago in 2005 were in parity and exchanged at the rate of Y109/$?

2)Consider the following short-run production function (where L = variable input, Q = output)

Q = 6L2 - 0.4L3 (2 and 3 are not numbers, its like an exponent to L, sorry don't know how to type like an exponent)

a)Determine the marginal product function (MPL)

b)Determine the average product function (APL)

c)Find the value of L that maximizes Q.

d)Find the value of L at which the marginal product function takes on its maximum value.

3) The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed:

Crew size Amount of Fish Caught Per Week

(Number Of Workers) (Hundreds of LBS)

2 3

3 6

4 11

5 19

6 24

7 28

8 31

9 33

10 34

11 34

12 33

a)Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?

b)How large a crew should be used if the trawler owneris interested in maximizing the total amount of fish caught?

c)How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per worker?

4)Consider Exercise 3 again. Suppose the owner of the trawler can sell all the fish caught for $75 per 100 pounds and can hire as many crew members as desired by paying them $150 per week. Assuming that the owner of the trawler is interested in maximizing profits, determine the optimal crew size.