Elementary Mathematical Techniques for Economics

Instructor: Ram Sewak Dubey ECON 317: Problem Set 8 December 3, 2018

1. [Income and Cross Price Elasticity of Demand]

(a) Given Q= 700−2P+0.02Y , where P= 25, and Y = 5000. Find (a) the price elasticity of demand and (b) the income elasticity of demand.

(b) Given Q1 = 100−P1 +0.75P2−0.25P3 +0.0075Y.

At P1 = 10, P2 = 20,P3 = 40 and Y = 10000, Q1 = 170. The cross price elasticity of demand for good 1 when price of good 2 is changing is given by

ε12 = (

∂Q1 ∂P2

) × (

P2 Q1

) .

The cross price elasticity of demand for good 1 when price of good 3 ε13 is defined in similar manner. Find th cross price elasticities of demand for good 1.

(c) Given Q1 = 50−4P1−3P2 +2P3 +0.001Y.

At P1 = 5, P2 = 7,P3 = 3 and Y = 11000, Q1 = 26.

(i) Find cross price elasticities of demand for good 1,

(ii) the income elasticity of demand,

(iii) Are good 1 and good 2 substitutes or complements?

(iv) Are good 1 and good 3 substitutes or complements?

(v) Determine the effect on Q1 of a 10 percent price increase for each of the other goods individually.

2. [Homogeneity and Returns to Scale]

Determined the level of homogeneity and returns to scale for each of the following pro- duction functions.

(a) Q = x2 +6xy+7y2.

(b) Q = x3− xy2 +3y3 + x2y.

Submission deadline: December 10, 2018 Page 1 of 2

Instructor: Ram Sewak Dubey ECON 317: Problem Set 8 December 3, 2018

(c)

Q = 3x2

5y2 .

(d) Q = 0.5K0.2L0.6.

(e) Q = 0.5K0.2L0.9.

(f) Q = 0.5K0.2L0.8.

(g) Q = 5K +3L.

(h) Q = min{5K,3L} .

(i) Q = AKαLβ,α > 0,β > 0.

Submission deadline: December 10, 2018 Page 2 of 2