Prof. Akbulut Answer Key - Problem Set 1 (10 points) 1. (2 pts.) For each of the following functions, calculate the derivative with respect to x. a. fx 2 4x 2 fx 8x fx 2e 5x let z 5x y 2e z fx dy/dzdz/dx 2e 5x 5 10e 5x fx e x x 2 fx de x /
Prof. Akbulut Answer Key - Problem Set 3 (10 points) (2 pts.) Let U x 1/3 y 2/3 be the utility function where x and y are two goods. p x and p y are respectively the prices of the two goods x and y, and M is the income of the consumer. (a) Derive th
Econ 102 Prof. Akbulut
Answer Key - Problem Set 4
(10 points)
1. (3 pts.) Nicholson Ch. 7, Problem 7.2 q = kl - 0.8k2-0.2l2 a) When k=10 q = 10l - 80 -0.2l2 maximum, MPl = 0. max. of the total product curve is at l = 25.
This is the total product
Lecture 14: Cost Functions
1
Contingent Demand for Inputs
Contingent demand functions for all of the firms inputs can be derived from the cost function
Shephard's lemma
the contingent demand function for any input is given by the partial derivati
Lecture 13: Cost Functions
1
Cost Minimization
Suppose that the production function is CES: q = (k + l )/ The Lagrangian expression for cost minimization of producing q0 is L = vk + wl + [q0 - (k + l )/]
2
Cost Minimization
The first-order condi
Lecture 12: Production Functions Cost Functions
1
Technical Progress
Suppose that the production function is q = A(t)f(k,l) where A(t) represents all influences that go into determining q other than k and l
changes in A over time represent techni
Lecture 11: Production Functions
1
Production Function
The firm's production function for a particular good (q) shows the maximum amount of the good that can be produced using alternative combinations of capital (k) and labor (l) q = f(k,l)
2
Mar
Prof. Akbulut Answer Key - Problem Set 2 (10 points)
1.
(2 pts.) Nicholson Ch. 4, Problem 4.2 I'll use a simpler notation for this problem: Uf, c f 2/3 c 1/3 a. Lagrangian: f 2/3 c 1/3 300 - 20f - 4c /f 2 c 1/3 - 20 0 3 f /c 1 c 2/3 - 4
Econ 102 Prof. Akbulut
Answer Key - Problem Set 5
(10 points)
1. (3 pts.) Nicholson Ch. 8, Problem 8.4 (a) q = min(5k, 10l) C=vk+wl=k+3l The cost function is a function of v, w, and q. Since we have values for v and w, it will be a function of q on