Question

1) The market demand for Brand x has been estimated as:

Qdx=1,500−3Px−0.05M−2.5Py+7.5PzQxd=1,500−3Px−0.05M−2.5Py+7.5Pz

where PxPx is the price of Brand x, M per capita income, PyPy is
the price of Brand y, and PzPz is the price of Brand z. Assume that
Px=$2,M=$20,000,Py=$4,andPz=$4Px=$2,M=$20,000,Py=$4,andPz=$4.

With respect to changes in per capita income, what kind of good is Brand x?

How are Brands x and y related?

How are Brands x and z related?

How are Brands z and y related?

What is the market demand for Brand x?

Answer #1

(1) Since coefficient of M (per capita income) is negative in demand function, with increase (decrease) in income, demand for Brand X decreases (increases), so it is an inferior good.

(2) Since coefficient of Py is negative in demand function, with increase (decrease) in price of good Y, demand for Brand X decreases (increases), so Brands X and Y are complements.

(3) Since coefficient of Pz is positive in demand function, with increase (decrease) in price of good Z, demand for Brand X increases (decreases), so Brands X and Z are substitutes.

(4) Since coefficient of Py is and Pz are of opposite sign in demand function, Brands Y and Z are complements.

(5) Plugging in given values,

Qdx = 1,500 − 3 x 2 − 0.05 x 20,000 − 2.5 x 4 + 7.5 x 4

Qdx = 1,500 - 6 - 1,000 - 10 + 30

Qdx = 514

The market demand for
brand X has been estimated as
Qx = 1,500 - 3Px -
0.05I - 2.5Py + 7.5Pz
where Px is
the price of brand X, I is per-capita income,
Py is the price of
brand Y,
and Pz is the price of brand Z. Assume that
Px = $2, I = $20,000,Py = $4, and
Pz = $4. a. With respect to changes in per-capita income,
what kind of good is
brand X?
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