Economics I, Departmental Honors (Sections 228, 229)
Instructor: Brandon Weber
Midterm I
October 7, 1999
Instructions:
n Answer all questions. You have 60 minutes for the exam. 50 minutes have been assigned for questions. The other 10 minutes are free.
n Write all answers in the provided blue books. Show all work. Use diagrams where appropriate and label all diagrams carefully.
n Write your name, recitation section, and my name on all blue books.
n Penn=s Honor System applies.
n Hand in all blue books at the end of the exam. You can keep your copy of the exam.
PART I. 20 Minutes (5 minutes per question)
For each question, indicate whether you think the statement is true, false, or uncertain and explain (regardless of the case).
1. Consider a two good (x and y), two country (I and II) economy. Suppose that the countries were previously unknown to one another and now decide to trade. If Country I produces more of good x per resource level than Country II, then Country II should decrease its production of x and purchase it from Country I.
2. The quantity demanded of a good decreases when people expect that the future price of the good will fall.
3. Given a linear supply curve (where the supply curve is not perfectly elastic or inelastic), the deadweight loss resulting from a unit sales tax is decreasing in the elasticity of the demand curve, i.e., the steeper the demand curve the greater the deadweight loss.
4. Consider the price effect for good x induced by a decrease in P_x (where P_x is the price of good x). Good x is said to be inferior if the price effect is greater than the substitution effect.
PART II. 10 Minutes (5 minutes per sub-question)
Suppose that the supply and demand curves for a good are given by the following equations:
Q_d = 20 B 4*P
Q_s = 2*P B 4,
where Q_d is the quantity demanded of the good, Q_s is the quantity supplied of the good, and P is the price of the good.
a. Calculate the equilibrium price and quantity. Now calculate the consumer and producer surplus.
b. Now suppose that the government imposes a price ceiling at P = 3. What is the equilibrium quantity? Calculate the new consumer and producer surplus and the resultant deadweight loss.
PART III. 20 Minutes (5 minutes per sub-question)
Suppose that the preferences of a consumer over goods x and y are represented by the following utility function:
U(x, y) = x + y,
where x and y indicate the quantity of goods x and y consumed, respectively.
a. Graph the indifference map for this utility function. (As usual, you only need to show a few indifference curves.)
b. What can you say about the cross-elasticity of demand of these two goods? What does this imply about these goods?
c. Now suppose that the consumer has the usual budget constraint:
W = P_x*x + P_y*y,
where P_x and P_y are the prices of good x and y, respectively, x and y are the quantities of good x and y consumed, respectively, and W is the wealth (a.k.a., budget or income) of the consumer.
Suppose that P_y > P_x. What is the optimal level of consumption of goods x and y?
d. Is it true that in this case (MU_x / P_x) = (MU_y / P_y), where MU_x and MU_y are the marginal utilities of x and y, respectively? Answer this using the slope of the budget line and the Marginal Rate of Substitution.