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 q

s = –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. 3

b. Now, find equilibrium q and p in three different ways:

(i) Graphically. Label the equilibrium values on the graph with q* and p*. (ii) Using the supply and demand equations. First, equate q

d to q

s 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 p

s,

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

The equation for the PPF is y = (100 – x2)

.5.

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)_____________