Problem Set 10B Sample Solutions
1. Consider a firm with cost function
900 if q = 0
C(q) = where q is the firms output.
2500+100q+025q2 ifq > 0
The firm acts as a competitive pricetaker.
a. Find its supply function,
b. Find the firms producers surplus as
Substitution Effects
Substitution Effects
Starting om some initial budget and optimal choice, (x*, y*), how might we
measure the income change necessary after a price change in order to make the consumer
as well off as originally?
In essence, the income a
Production Functions
Production
A large part of the material on production and cost is quite similar to the previous
material on consumer utility functions and optimal choice. The terminology is different.
The bundle of inputs, (21, 22) is used to produce
Cost Relationships
Relationship Between Short-run Cost Curves and Product Curves
Given the xed level of 22, let 2* (y) denote the amount of input 1 needed to produce
output y (i.e.,f(Z*(y), 22) = y). Then
AP1(Z*O)Z*0) =y,
the short-run variable cost to pr
Consumer Theory
Income Consumption Curve
For xed prices, p and q, the Income Consumption Curve (or Path) is the
collection of optimal bundles corresponding to all the different possible income levels.
The xed prices determine the slope of the budget line
Consumers Surplus
Consumers Surplus with Discrete Choice
First consider a discrete version of the problem, in which the rst good must be
consumed in integer amounts.
Suppose the consumer could use only one unit of the good, so the choice is between
zero u
Problem Set 10B Sample Solutions
1. Consider a firm with cost function
900 if q = 0
C(q) = where q is the firms output.
2500+100q+025q2 ifq > 0
The firm acts as a competitive pricetaker.
a. Find its supply function,
b. Find the firms producers surplus as
Problem Set 6 Sample Solution
Problems 1 3 concern firms that use two inputs, (z1,z2) to produce one output, y,
according to a production function f(z1, zz). The firms face perunit prices W1 and w2 for the
inputs.
1. Firm 1 has production function f(z1, z
Problem Set 7 Sample Solution
1. Consider three firms that use labor and capital to produce their outputs. Each firm
produces a different good. Firm 1 uses L1 and K1 to produce widgets according to the production
function Q1 = (L1K1)02 . Firm 2 uses L2 an
Problem Set 10 Sample Solution
This problem set consists of practice problems for the second midterm. Problems 1 ~ 5
made up the 2013 exam. Problems 6 - 8 are additional, related problems.
The second exam covers the course material through the end of the
Professor Mumford
mumford@purdue.edu
Econ 562 - Fall 2015
Problem Set 8
Due by 11:59 PM Eastern on Friday, October 16
Please type your answers and combine them into a single document. You will likely need
to use an equation editor. Save your file either a
Problem Set 11 Sample Solution
1. A monopolist with cost function C(q) = 25,000 +100q + 0.25q2 for q > 0 and 0(0) 2 0,
. . 20 0 4
where q is the firms output, faces aggregate demand D(p) = 038 forp 5 500' The
monopolist sets a perunit price and consumers
Introduction to Main Tools
Models
What is a model? It is a simplied version of a real-world situation.
Specics of the model depend on the questions to be addressed. This involves the art
of including the important features of the real-world situation With
Problem Set 9 Sample Solution
1. Consider a single firm with cost function c(q) = 225 +10q + q2 for q > 0 and c(0) = 0,
where q is the firms output. Aggregate demand is D(p) = 3200 51).
a. What is the firms supply function?
b. If all firms have access to
Problem Set 6 Sample Solution
1. There are three consumers. Demand for the first consumer is d1(p) = 200 p for p < 200
and zero elsewhere. Demand for the second consumer is d2(p) = 320 2p for p < 160 and zero
elsewhere. Demand for the third consumer is d3
Problem Set 15 Due Wednesday, December 5
1. An individual with endowment (1500, 5000) has access to a perfect capital market with
interest rate 25% per year. She also has access to a private investment opportunity. If she invests
$2: > 500 in the private
Problem Set 11 Due Wednesday, October 31
1. Freedonia is the only country in which individuals consume widgets, but widgets are
produced both inside and outside Freedonia. The market is competitive within Freedonia with
demand D(p) = 1000 4p for p s 250,
Problem Set 14 Due Wednesday, November 28
1. Consider a market with aggregate demand Q = 40 21) (where Q is the amount demanded
and p is the market price) and two firms. Each firm has cost function C(q) = 0.5q2, where q is the
output of the firm. The firm
Problem Set 13 Due Wednesday, November 14
1. Consider a market with a dominant firm and a competitive fringe made up of 150 price
taking firms. Each firm in the fringe has cost function C(q) = 3q2, the dominant firm has cost
function C(q) = 0.02q2 and mar
Problem Set 12 Due Wednesday, November 7
1. Consider a market with a dominant firm and a competitive fringe made up of 100 price
taking firms. Each firm in the fringe has cost function C(q) = cf, the dominant firm has cost
function C(q) = q2 /60 and marke
Problem Set 5 Due Wednesday, September 19
1. Holding income and the price of good two fixed, Ardens demand for good one can be
expressed as
x = 2500 50p forp s 50 [and 0 for p > 50]
where p is the price of the good and x is the quantity demanded. Her inco
Problem Set 3 Due Wednesday, September 5
1. For utility function u(x, y) = 5x + y
a. Find the Income Consumption Curve (ICC) when prices are p = 10 and q = 5.
b. Find the Price Consumption Curve (PCC) when income is m = 100 and the second good
has price q
Problem Set 9 Due Wednesday, October 17
1. Consider a market in which all firms have access to a technology with cost function
C(q) = 100 + 40q + q2 for q > 0 and C(0) = 0, where q is the firms output. This cost function
applies in both the short and long
Problem Set 8 Sample Solution
1. A firm has two plants that it may use to produce its output. The first plant has cost
function C1(Q1) = Q12 and the second plant has cost function C2 (Q2) = Q2 + 0.5Q22 .
a. If total output to be produced, Q1 + Q, must be
Problem Set 10
This problem set consists of practice problems for the second midterm. All problems
appeared as midterm problems within the last few years. [Problem 3 of Problem Set 7 was also a
recent exam question]
The second exam covers the course mater
Problem Set 8 Sample Solution
1. A firm has two plants that it may use to produce its output. The first plant has cost
function C1 (Q) = Q12 and the second plant has cost function C2 (Q) = Q2 + 0.5Q22 .
a. If total output to be produced, Ql + Q, must be Q
Problem Set 6
Problems 1 3 concern firms that use two inputs, (z1,z2) to produce one output, y,
according to a production function f(z1, zz). The firms face perunit prices w1 and w2 for the
inputs.
1. Firm 1 has production function zl, zz) = zlzz.
a. What
Problem Set 4 Sample Solution
1. Tosca has an endowment consisting of both leisure time and a dividend payment, has
preferences over bundles of leisure (x) and money for consumption of all other goods at fixed
prices ()2), and is free to choose the number