ECO 303

MIDTERM 1.

QUESTION 1 (50 pts)

Suppose that there is a consumer who consumes 2 types of goods: Good 1 and Good 2. The consumer has $96 and the price per unit of Good 1 is $3 and the price per unit of Good 2 is $8. However, the consumer is not completely free in making decisions as he is restricted by some policy rules. The government restricts the consumer in the following way: If he/she consumes more than 4 units of Good 2, he/she gets 40% subsidy per unit of Good 2 consumed in excess of 4 units. Also, the maximum amount of Good 2 that can be consumed is 9 units. There is no restriction on the consumption of Good 1.

a) Draw the budget line with either Good 1 on the vertical axis or Good 2 on the vertical axis. Clearly state the intercept points with the axes and the critical kink points if there are any.

b) Find the optimal consumption point (x1*, x2

*) if the consumer’s preferences are represented by the following utility function: U(x1,x2)=9x1+x2.

(Hint: When we have imperfect substitutes we have 3 possibilities for optimum: Vertical intercept of the budget line (unique optimum), horizontal intercept of the budget line (unique optimum) and the whole budget line (infinitely many optima). But this rule holds only for smooth budget lines. However, now we may have kink points on the budget line. This is why, although we still have imperfect substitutes case, the unique optimum point may be an interior point.)

QUESTION 2 (25 pts)

Suppose that there is an ordinary monopolist who faces a demand for apartments given by D(p)=100-5p. The monopolist also has a cost of renting his/her apartments and this cost is given by C(p)= 40p+p2. How much would he charge for the apartments if he has 80 apartments? What would the level of his profit be?

QUESTION 3 (25 pts)

Suppose that a consumer’s preferences are given by U(x1, x2 )= ln(3x12)+x2. Find the optimal

consumption bundle (x1*, x2

*) if he/she faces the following prices and budget: p1=2, p2=4 and m=32. Also calculate the Utility Level at (x1

*, x2*).