I've been out of school for quite sometime now and I'm trying to get
back into it to finish my degree, however I'm practicing to take this
progress exam so they know where I stand and what I'm capable of.  Out
of this book I'm using I can't understand the concept and need help
with solving the problem.  Please show the steps used to solve the
question as well as the final outcome.

Q1)   The market demand for cotton socks is given by:

Q=1,000+.5I-400P+200P?

where,
Q = Annual demand in number of pairs
I = Average income in dollars per year
P = Price of one pair of cotton socks
P? = Price of one pair of wool socks

Given that I = $20,000, P=$10, and P?=$5, determine:

A.	The price elasticity, e(Q,P)
B.	The income elasticity, e(Q,I)
C.	The cross price elasticity, e(Q,P?)



Q2)   Frisbees are produced according to the production function

q=2K+L

where,
q = Output of Frisbees per hour
K = Capital labor input per hour
L = Labor input per hour

A.	If K=10, how much L is needed to produce 100 frisbees per hour?
B.	If K=25, how much L is needed to produce 100 frisbees per hour?
C.	What is the RTS along the q=100 isoquant?
D.	Suppose technical resulted in the production function for Frisbees
becoming, q=3K+1.5L.  Answer parts A-C again using this new production
function.

Q1) a. Price elasticity = (dQ/dP)*P/Q = -400
[P/(200P'-400P+0.5I+1000)] = -400 [10/(200*5 - 400*10 + 0.5*20000 +
1000)] = -0.5.

b. Income elasticity = (dQ/dI)*I/Q = 0.5 [I/(200P'-400P+0.5I+1000)] =
0.5 [20000/(200*5 - 400*10 + 0.5*20000 + 1000)] = 1.25.

c. Cross-price elasticity = (dQ/dP')*P'/Q = 200
[P'/(200P'-400P+0.5I+1000)] = 200 [10/(200*5 - 400*10 + 0.5*20000 +
1000)] = 5.

Sources:  

"Using Calculus To Calculate Price Elasticity of Demand" by Mike
Moffatt, About, Inc. (2006)
http://economics.about.com/cs/micfrohelp/a/calculus_d.htm

"Using Calculus To Calculate Income Elasticity of Demand" by Mike
Moffatt, About, Inc. (2006)
http://economics.about.com/cs/micfrohelp/a/calculus_i.htm

"Using Calculus To Calculate Cross-Price Elasticity of Demand" by Mike
Moffatt, About, Inc. (2006)
http://economics.about.com/cs/micfrohelp/a/calculus_c.htm

Q2) a. 100 = 2(10) + L => L = 80
b. 100 = 2(25) + L => L = 50
c. RTS = MPL/MPK.  MPL = dq/dL = 1.  MPK = dq/dK = 2.  Therefore, RTS = 1/2 = 0.5.
c. 100 = 3(10) + 1.5L => L = 46.67
100 = 3(25) + 1.5L => L = 16.67
RTS = (dq/dL)/(dq/dK) = 1.5/3 = 0.5.

Source:  "Problem Set 6 Answer Key" Lanjouw, UC Berkeley (Fall 2004)
http://are.berkeley.edu/courses/EEP100/fall2004/Homework/prob6_2004_anskey.pdf
Page 3, part e)

Sincerely,

Wonko

A little later than expected, but all the answers are correct and it
does show how they were completed, so no complaints.