Chapter 1
ECONOMIC MODELS
key concepts
Marshallian supply-demand synthesis
economic model:
assumptions
verification
equilibrium:
partial
general
ceteris paribus
optimization
normative vs. positive
value:
in use
in exchange
labor theory
marginalism
comparative statics production possibility frontier
opportunity cost
t.i.n.s.t.a.a.f.l. (popular abbreviation for “there is no such thing as a
free lunch”)
problems
(Numbers in brackets at the beginning of problems below refer to related examples and problems
in the text.)
2
PART I Introduction
1.1. [Related to text example 1.2.] Consider the following supply and demand curves:
qd = 300 – 20p
qs = –100 20p
a. In graphs of supply and demand curves, it is conventional to put price on the
vertical axis and quantity on the horizontal axis. In mathematics, it is
conventional to put the variable from the left-hand side of an equation on the
vertical axis of a graph. Since you are accustomed to the latter convention, it
will be easier for you to draw graphs of supply and demand curves if you first
invert them; that is, solve for p as a function of q. For the demand curve
above, subtract 300 from both sides then divide both sides by –20 to get:
pd = 15 – q/20
Note that the subscript d is now attached to p, rather than q. It is not necessary to make this
switch, but it is consistent with the interpretation of the inverse demand function to do so. The
inverse function tells us the highest price that consumers are willing to pay (demand price) for
quantity q. What is the vertical intercept of the line that is described by this equation?
(1)_________________ What is the slope of this line? (2)___________________ How is the
slope of the line related to the coefficient of p in the original equation?
(3)___________________ Draw the line on the diagram below and label it d.
Now, find the inverse of the supply function.
Economic Models CHAPTER 1 3
ps = (4)__________________________
What is the interpretation of the inverse supply function?
(5) ________________________________________________________________
What is the vertical intercept of the line that is described by this function?
(6)_______________ What is the slope of this line? (7)__________________ How is the slope
of the line related to the coefficient of p in the original equation?
(8)_______________________ Add this line to the diagram above and label it S.
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b. Now, find equilibrium q and p in three different ways:
(i)
(ii)
Graphically. Label the equilibrium values on the graph with q* and p*.
Using the supply and demand equations. First, equate qd to qs and solve for p*.
Now substitute the value you obtained for p* into the demand equation and solve for
q*.
Check your solution by substituting the value you obtained for p* into the supply
equation and confirming that you get the same value for q*.
(iii) Using the inverse supply and demand equations. Determine q* first by equating pd to ps,
then determine p by substituting q* into the inverse demand equation, and finally check
your solution by substituting q* into the inverse supply equation.
Be sure that you understand why all of these methods yield the same solution. You will
have numerous occasions to use them in this workbook and the text. Often one method
will be much simpler than the other two.
c. Suppose that the demand curve shifts to qd = 380 – 20p. At any value of P, this new demand
curve is (1)_____________ units to the right of the old curve. Add the new curve to the graph,
4
PART I Introduction
label it D', and determine the new equilibrium values for p and q by any method you wish.
(Try all three if you had any trouble with b.)
q* = (2)_________________ p* = (3)_________________
d. Suppose that the supply curve shifts to qs = –180 + 20p. At any value of P, this new
supply curve is (1)______________ units to the right of the old curve. Add the new
curve to the graph, and label it S'. Using the original demand curve, determine the new
equilibrium values for p and q by any method you wish.
q* = (2)_________________ p* = (3)_________________
e. If you observed a price increase in a market, how would you know whether it was due
to a shift in demand or a shift in supply?
1.2. [Related to text example 1.3.] A production possibility frontier (PPF) for goods x and y is
depicted in the diagram below.
Economic Models CHAPTER 1 5
2 .5
The equation for the PPF is y = (100 – x ) .
a. If x = 6, what is the most y that can be produced? (1)__________________ What is the
opportunity cost of x in terms of y? [There are two ways to find it. One way uses the line that
is tangent to the PPF at x = 6. The second way uses the derivative of y with respect to x. If
your derivatives are rusty, you may want to come back to this after completing Chapter 2.]
(2)__________________
b. Repeat a for x = 8. (1)_____________ (2)_____________