Question

7. Suppose you know that a demand function of consumer for good 1 is p-, where pi is price of the good and xi is the quantity consumed. You know that the consumer can buy only good 1 or good 2. Her income is $2000 and the price of good 2 is P2 〉 0. (a) Find an utility function that represents the preferences of this consumer (b) Given the above utility function derive demand for good 2. (c) Suppose that there are 100 consumers indexed by i with preferences represented by the utility function in question a). Suppose that income of consumer i -1,2,3,..., 100 is mi-1000 + 100i. Find a market demand function for each good (total consumer demand as a function of price).

Answer 1

(a) Yes, law of demand holds, since the coefficient of own price in the demand function is negative, signifying as own price increases (decreases), quantity demanded decreases (increases).

(b) Yes, law of supply holds, since the coefficient of own price in the supply function is positive, signifying as own price increases (decreases), quantity supplied increases (decreases).

(c) Goods X & Y are substitutes, since coefficient of price of Y in demand function is positive, signifying that as price of Y increases (decreases), demand for X increases (decreases).

(d) Goods X & Z are complements, since coefficient of price of Z in demand function is negative, signifying that as price of Z increases (decreases), demand for X decreases (increases).

(e) X is a normal good, since coefficient of income in demand function is positive, signifying that as income increases (decreases), demand for X increases (decreases).

(f)

Qxd = 100 – 2PX + 0.01M + 8 PY - 4Pz = 100 - 2PX + (0.01 x 2,000) + (8 x 10) - (4 x 5)

Qxd = 100 - 2PX + 20 + 80 - 20

Qxd = 180 - 2PX

NOTE: First 6 sub-parts are answered.