ECO 420k
Summer I 2017
1. Find the own-price elasticity of demand for gasoline if the demand function is 0.5 x=20/ P x . Plot the demand function (with price on the upper axis and x on the lower axis) for x=2, 4, 6, and
8. Derive a function for total spending (xP x) given this demand function, and differentiate with
respect to Px. Use the plots to show how spending changes from x=2 to x=4.
2. Suppose demand for movies is given by x=80 /P x . If a tax is placed on movies so that the price of movies increases from $10 to $15, what is the lost consumer surplus? Draw a demand
graph and sketch out the lost surplus area.
3. Kate spends her weekly income of $30 on chocolate (x) and tacos (z). Initially, when the prices
are Px = Pz = $2, she buys x=10 and z=5. After the prices change to P x = $1 and Pz = $3, she
purchases x=6 and z=8. Draw her budget lines and choices on a diagram. Use a revealed
preference argument to discuss whether she is maximizing utility before and after the price
changes.
4. Nicholson (12th edition), Problem 9.2:
Suppose the production function for widgets is given by q = kl – 0.8k 2 – 0.2l2, where q represents
the annual capital input, and l represents annual labor input.
a. Suppose k = 10; graph the total and average productivity of labor curves. At what level of
labor input does this average productivity reach a maximum? How many widgets are
produced at that point?
b. Again assuming that k = 10, graph the MP l curve. At what level of labor input does MP l =
0?
c. Suppose capital inputs were increased to k = 20. How would your answers to parts (a)
and (b) change?
d. Does the widget production function exhibit constant, increasing, or decreasing returns
to scale?
5. Nicholson (12th edition), Problem 9.4, Part a (hint: equate MPL at the two places):
Suppose that the production of crayons (q) is conducted at two locations and uses only labor as
an input. The production function in location 1 is given by q 1 = 10l10.5 and in location 2 by q2 =
50l20.5.
a. If a single firm produces crayons in both locations, then it will obviously want to get as
large an output as possible given the labor input it uses. How should it allocate labor
between the locations to do so? Explain precisely the relationship between l 1 and l2.
b. Assuming that the firm operates in the efficient manner described in part (a), how does
total output (q) depend on the total amount of labor hired (l)?

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