University of Wisconsin
Economics 301:
Intermediate Microeconomic Theory
Korinna K. Hansen
Practice Problems (Part 2)
1). Use graphs where necessary and EXPLAIN whether the following statements are true or false:
a). If the price of insurance goes up, people will become less risk averse.
b). If consumer 1 has the demand function x
1
= 1,000 - 2p and consumer 2 has the demand
function x
2
= 500 – p, then the aggregate demand function for an economy with just these two
consumers would be
x = 1,500 – 3p
for p<500.
c). If the elasticity of the demand curve for barley is –1.5 at all prices higher that the current
price, we would expect that when bad weather reduces the size of the barley crop, total revenue
of barley producers will fall.
d). The demand function for potatoes is x = 1,000 – 10p.
As the price of potatoes changes from
10 to 20 cents, the absolute value of the price elasticity of demand for potatoes increases.
e).
If the demand curve for a good is given by the equation x=2/p, where x is quantity and p is
price, then at any positive price, the elasticity of demand will be –1.
f). If consumer 1 has the inverse demand function given by p= 15 –x and consumer 2 has the
inverse demand function given by
p = 20 – 3x, then the total quantity demanded by the two
consumers is x = 7 when the price p = 11.
g). The demand curve, which is a downward-sloping straight line, crosses the supply curve,
which is an upward-slopping straight line.
If a tax is introduced where sellers must pay a tax of
$2 per unit sold, then the equilibrium price paid by demanders will rise by more than $1 if the
absolute value of the slope of the demand curve is greater than the absolute value of the slope of
the supply curve.
h). Assume that the amount of a good supplied is independent of the price.
Then, if a sales tax is
imposed on the good, the price paid by consumers will increase by a lot.
i). If the production function is f(x
1
, x
2
) = min (2x
1
+x
2
, x
1
+2x
2
), then there are increasing returns
to scale in this technology.
j). For a firm with two variable factors and a production function f(x
1
, x
2
) = (2x
1
+ 4x
2
)
1/2
, the
technical rate of substitution between x
1
and
x
2
is constant (does not change as output changes).
k). A firm uses two inputs to produce its output.
The inputs are perfect substitutes.
Therefore
this firm must always have constant returns to scale.
l).
When there is increasing returns to scale, the average cost is a decreasing function to output.