100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Micro - Exam 2014 - Questions & Answers $3.21   Add to cart

Exam (elaborations)

Micro - Exam 2014 - Questions & Answers

 1608 views  0 purchase
  • Course
  • Institution

The exam of 2014 with the official answers

Preview 1 out of 9  pages

  • May 11, 2016
  • 9
  • 2014/2015
  • Exam (elaborations)
  • Questions & answers
avatar-seller
Note. These answer keys give more detail than you were expected to write down. You should skip
some of the intermediate skip for space.


Part I: Weeks 1 through 3
1. Technology and Profits. [14 pts.]

(a) Calculate the degree of homogeneity in the CES case
1 1
q = f (z1 , z2 ) = (αz12 + (1 − α)z22 )4

where q is output and z1 and z2 are inputs, all other symbols are parameters. Does a
characterization of the returns to scale depend on the size of the scaling factor (i.e., t ≥ 1
or t < 1)? [5]
(b) Consider a two-input Cobb Douglas function that has increasing returns to scale. Is this
compatible with decreasing marginal products? Support your answer with a calculation.
It is okay to consider a specific example. [6]
z2

(c) Consider the map of isoquants on the right. In a thought
experiment, we superimpose an iso-profit plane on it that
just touches the production frontier along many points—
depicted as dashed vertical line. Can such a pattern be ob-
served when the technology is of the Cobb Douglas form?
Motivate your answer. [3] z1

ANSWER

(a) Using scaling factor t and applying rules of elementary algebra, we find
1 1 1 1 1 1
f (tz1 , tz2 ) = (αt 2 z12 + (1 − α)t 2 z22 )4 = t2 (αz12 + (1 − α)z22 )4 = t2 f (z1 , z2 )

Homogeneous of degree 2. If t = 0.5, then 0.52 = 0.25 < 1, but since we are shrinking the
scale, this is compatible with increasing returns to scale.
common mistakes and difficulties
1 1
• f (tz1 , tz2 ) = (α · t · z12 + (1 − α) · t · z22 )4
• f (tz1 , tz2 ) = α4 · t2 · z21 + (1 − α)4 · t2 · z22
• various other problems associated with elementary rules of algebra (esp. how to deal
with exponents)
• misperception of tr indicating IRTS because t > 1 (instead of r > 1)
(b) Yes: Without loss of generality
q = z1α zr2−α , α>0
and r > 1 for returns to scale to increase. Marginal product for, say input 2 is

∂q
= (r − α)z1α zr2−α z2−1 = q(r − α)/z2
∂z2


1

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller jipclaassens. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $3.21. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

67474 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$3.21
  • (0)
  Add to cart