AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
Chapter Two
Equations statement where two expressions are equal Slope change in the dependent variable divided by the change in the independent variable o If X changes by one units, Y changes by m units o M is a parameter and multiplier In tercepts o XI
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
AEB 3510 PROBLEM SET 3: APPLICATIONS OF PARTIAL DERIVATIVES 1. Solution: (a) The marginal productivity of labor is given by:
f ( x, y) x
40 x 3 y
(b) The marginal productivity of capital is given by:
f ( x, y ) y
3x
(c) When x=250 and y=100, the marginal
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
AEB 3510 Chapter 10: Supplemental Problems ANSWER KEY
1. Solution:
a) The Total Revenue function for the toll road is given by
b) We want to maximize revenues:
The revenue function must be concave in order to be maximized:
d 2 R( p) dp 2 500 0
Hence, the
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
Solutions to Extra Problems for Chapter 9: Question 1 1a. TR' (Q) 0.2Q 4.5 . This derivative represents the change in total revenue resulting from a change in output. In economics, this concept is called Marginal revenue. 1b. TR' (15) 0.2(15) 4.5 1.5 . If
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
Extra Problems Chapter 9
1.
The Total Revenue function for a milk producer is given by
TR(Q) 0.1Q 2 4.5Q 35,
where Q is the quantity of milk demanded (in pounds) and P is the unit price of milk. a) Find the derivative of the Total Revenue function. deriva
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
Extra Study Problems, Chapter 3
1. Suppose that for a firm, the demand function can be expressed as
P(Q ) = 20 0.05Q
and
( P, Q) = 20 P 0.56Q 2 50Q 65 ,
where P is price and Q is output. Find (Q) .
2. The demand for chicken is given by the demand functio
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
AEB3510
Supplement Chapter 3
1. An importer of Brazilian coffee estimates the demand for coffee to be
Q( p) =
64800 p2
where p is price in dollars per pound. The price of coffee is estimated to be a function of time, t, as measured in weeks. The price per
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
AEB 3510, Extra Problems Chapter 9 1. The Total Revenue function for a milk producer is given by TR(Q) = 0.1Q2 +4.5Q +35, Where Q is the quantity of milk demanded (in pounds) and P is the unit price of milk. a) Find the derivative of the Total Revenue fu
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
Extra Problems Chapter 9 1. The Total Revenue function for a milk producer is given by TR(Q) = 0.1Q2 +4.5Q +35, Where Q is the quantity of milk demanded (in pounds) and P is the unit price of milk. a) Find the derivative of the Total Revenue function. Wh
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
AEB 3510: APPLICATIONS OF DERIVATIVES Chapter 10 Supplemental Problems 1) A toll road averages 35,000 cars per day. Suppose that the Department of Transportation estimates the demand function for the tollroad to be Q(p) = 60000 250p, where Q is the number
AEB3510 – Quantitative Methods in Food and Resource Economics
AEB 3510

Spring 2011
Chapter 13 Handout: Multivariate Optimization Let z = f(x, y) and let (xc , yc ) be a critical point of f(x, y) For (xc , yc ) to be a Local Maximum, then 1. fx = 0 fy = 0 Must hold as a system, i.e., you have to solve it as a system. [this identifies (xc