Brandon Weber

Economics I, Departmental Honors (Sections 233, 234)

Instructor: Brandon Weber

Midterm I

October 12, 1999

Instructions:

Answer all questions. You have 60 minutes for the exam. 50 minutes have been assigned for questions. The other 10 minutes are free.

Write all answers in the provided blue books. Show all work. Use diagrams where appropriate and label all diagrams carefully.

Write your name, recitation section, and my name on all blue books.

Penn’s Honor System applies.

Hand in all blue books at the end of the exam. You can keep your copy of the exam.

PART I. 20 Points (10 points per question)

For each question, clearly explain your answer.

Suppose that the demand function for good x is x = W / P_x, where x is the quantity of good x demanded, W is wealth, and P_x is the price of x. What is the elasticity of demand? Do not appeal to calculus.
Consider a two good economy where a consumer spends all her income on goods x and y. Suppose that the price of x increases and that the consumer decreases her consumption of both goods. Which if any of the goods are normal?

PART II. 30 Points (10 points per sub-question)

Suppose that there are two consumers whose inverse demand functions are given by the following:

P = 60 – 2*q₁,

P = 100 – q₂,

where q_i is the quantity demanded of the good by consumer i. Suppose that the supply of the good is given by

P = 2*Q_s – 40,

where Q_s is the quantity supplied.

Calculate the equilibrium price and quantity.
Calculate the consumer surplus.
Now suppose that the government imposes a per unit tax of $80. What is the new supply curve? What is the new equilibrium quantity and price?

PART III. 30 Points (10 points per sub-question)

Suppose that the TU function for a good is given by:

TU = 25*q – .5*q²,

where q is the quantity consumed. In turn the marginal utility function is given by:

MU = 25 – q.

Suppose throughout that the ratio of the marginal utility to price of all other goods is 1.

What is the demand function for this good? Graph it.
Suppose that the equilibrium price is P^* > 0 (a number). What is the consumer surplus as a function of P^*?
Show that the consumer surplus is equal to the total utility minus the total expenditure.

PART IV. 20 points (10 points 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) = min{2 * x + y, 2 * y + x},

where x and y indicate the quantity of goods x and y consumed, respectively, and

min{2 * x + y, 2 * y + x} means the minimum over 2 * x + y and 2 * y + x.

For example, U(1, 2) = min{4, 5} = 4.

This consumer has the usual budget constraint with wealth denoted by W. The prices of goods x and y are given by P_x and P_y, respectively.

Graph the indifference map for this utility function. (As usual, you only need to show a few indifference curves.)
What is this consumer’s optimal level of consumption of (demand for) goods x and y as a function of W, P_x, and P_y? Consider the following price ratios: P_x/P_y = 1, P_x/P_y = 2, P_x/P_y = ½, P_x/P_y > 1 (but not equal to 2), and P_x/P_y < 1 (but not equal to ½).