Download Old Midterm 2

Econ 301
April 5 2004
Peter Norman
Midterm 2
You have 75 minutes. It is indicated below how much each question is worth, so you should allocate your
time accordingly. Good Luck!
1. (20 points) Consider a consumer/worker with preferences over consumption and leisure. In a carefully
labeled indifference curve graph, decompose the effect on the labor supply for the worker in terms of
income and substitution effects. Also state whether you have drawn the graph assuming that leisure is a
normal or an inferior good.
2. (30 points) Joe owns a ranch where he produces (grass-fed) beef using two factors of production: land and
labor. Due to a long-term lease agreement, the quantity land is fixed for the relevant planning horizon.
1. (10 points) Introduce some notation for land, labor, the price of beef, the wage rate per unit of labor,
and the rental rate of land (state clearly what each variable means). Also introduce some notation
for the relationship between the factor uses and the output of beef and formulate the relevant profit
maximization problem for Joe (assuming land use is fixed)
2. (5 points) Assume that the marginal product of labor is decreasing. Depict the production possibilities
set (given fixed use of land).
3. (10 points) Very carefully, illustrate the solution to the profit maximization problem graphically.
4. (5 points) Due to a sudden boom in the economy, the wage rate is increased. Show graphically the
effect on Joes’ demand for labor and production of beef.
3. (25 points) Tweedeldum and Tweedeldee consume two goods only: weekday wireless minutes and weekend
wireless minutes. Tweedeldum has signed on with a service that gives him 1000 weekday minutes, but
no weekend minutes and Tweedeldee has a service that gives him 1000 weekend minutes, but no weekday
minutes. If you want to make life easy, assume that weekday minutes cannot be used in the weekend and
the other way around.
1. (10 points) In a carefully labeled graph, put in the endowment described above together with
some preferences for Tweedeldee and Tweedeldum. Draw the preferences in such a way that both
Tweedeldee and Tweedeldum prefers 500 weekday minutes and 500 weekend minutes to their initial
endowment.
2. (10 points) Explain carefully what a competitive equilibrium is in this environment and illustrate
how a competitive equilibrium would look like graphically in a NEW GRAPH. Don’t change the
preferences or the endowment!
3. (5 points) Consider the following alternative trading institution. Tweedeldum first suggests an allocation. Then Tweedeldee either agrees, in which case they consume the allocation suggested by
Tweedeldum. If Tweedeldee doesn’t agree, they both consume their respective endowments. In a
new graph, show how Tweedeldum will choose the allocation. Will this trading institution result in
a Pareto Optimal equilibrium?
ONE MORE QUESTION NEXT PAGE
4. (25 points) The hot dog vending industry in New Orleans is highly competitive. To produce hot dogs one
needs buns (x1 ), wieners (x2 ), mustard (x3 ), ketchup (x4 ), relish (x5 ), and raw onions (x6 ). Moreover, one
needs a little hot dog cart (x7 ), and, finally, workers (x8 ) to take care of the actual vending. Suppose the
cost of the raw materials are:
Input
Cost
$0.15
1 bun (x1 )
$0.50
1 wiener (x2 )
1 unit mustard (x3 ) $0.05
1 unit ketchup (x4 ) $0.05
1 scoop relish (x5 ) $0.10
$0.15
raw onions (x6 )
New Orleans customers only want hot dogs prepared with all the ingredients above. Moreover, there is
always a line at the hot dog stand and a hot dog vendor serves exactly 30 customers an hour. Finally, hot
dog vendors can be hired at $6 an hour and firms can rent hot dog carts at rate $9 an hour. Notice that
no hot dogs can be produced if there is no worker or no cart.
1. (10 points) Write down a production function in terms of x1 , ...., x8 that fits the description of the
technology above.
2. (5 points) Formulate the profit maximization problem for a hot dog vending firm.
3. (10 points) What is the equilibrium price of a hot dog in New Orleans? Hint: Taking derivatives
will do you no good!