ps1_101_2011_1

ps1_101_2011_1 - q boomerangs (i.e., what is the rms cost...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Economics 101 Problem Set 1 January 16, 2011 George J. Mailath Due Thursday, January 20, 2011 Please indicate your recitation time and recitation instructor on your answer. 1. The firm Oz Productions makes boomerangs. Its cost function is given by C ( q ) = 1 3 q 3 , where q is the quantity of boomerangs produced. (a) Calculate the firm’s supply curve (i.e., what is the profit-maximizing choice of q as a function of the price of the good, q * ( p ))? (b) How does the profit-maximizing quantity change in response to price changes, i.e., what is the slope of the supply function cal- culated in part 1(a) ? (c) Directly verify that this slope is also given by the formula dq * ( p ) dp = 1 C ±± ( q * ( p )) we derived in the first lecture. 2. Suppose boomerangs are produced using a single input, labor, accord- ing to the production function q = f ( ± ) = (3 ± ) 1 / 3 , i.e., a quantity ± of labor will produce (3 ± ) 1 / 3 boomerangs. Suppose the price of labor is w . (a) How much labor is needed to produce q boomerangs? (b) How much does it cost the firm to produce
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: q boomerangs (i.e., what is the rms cost function)? (c) What is the prot-maximizing choice of q as a function of the price of labor, q * ( w )? (d) How does the prot-maximizing quantity change in response to changes in w ? (e) Directly verify that this change is also given by the formula dq * ( w ) dw = [ f ( f 1 ( q * ( w )))] 2 wf ( f 1 ( q * ( w ))) we derived in the rst lecture. 1 3. Nicholson and Snyder problem 2.6. 4. Maximize the following: (a) 4 + x 1 3 x 2 3 x 1 x 2 x 2 1 4 x 2 2 . (b) 4+ x 1 3 x 2 3 x 1 x 2 x 2 1 4 x 2 2 subject to the constraint x 1 = 2 x 2 . (c) x 1 + x 2 subject to the constraint 1 x 1 + 2 x 2 = 2. (d) x 1 x 2 subject to x 1 + 3 x 2 = 4. (e) log x 1 + log x 2 subject to x 1 + 3 x 2 = 4. (Note that log is the natural log, i.e., base e ). (f) Is there a connection between your answer to parts 4(d) and 4(e) ? 2...
View Full Document

Page1 / 2

ps1_101_2011_1 - q boomerangs (i.e., what is the rms cost...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online