Elementary math tech for econ

Instructor: Ram Sewak Dubey ECON 317: Problem Set 3 October 4, 2018

1. [Market Equilibrium I]

Find the equilibrium price and quantity for the following markets.

(a)

Qd = 220−5P Qs =−20+3P.

(b)

Qd −128+9P = 0 Qs +32−7P = 0.

2. [Market Equilibrium II]

Find the equilibrium price and quantity for the following related market for two goods.

(a)

Qd1 = 82−3P1 +P2 Qs1 =−5+15P1.

and

Qd2 = 92+2P1 −4P2 Qs2 =−6+32P2.

(b)

Qd1 = 410−5P1 −2P2 Qs1 =−60+3P1.

and

Qd2 = 295−P1 −3P2 Qs2 =−120+2P2.

Submission deadline: October 10, 2018 on Canvas Page 1 of 3

Instructor: Ram Sewak Dubey ECON 317: Problem Set 3 October 4, 2018

3. [Market Equilibrium III]

Supply and demand functions could take non-linear form. In this question we examine such cases again to find the equilibrium price and quantity.

(a) Demand

P+Q2 +3Q−20 = 0,

and supply

P−3Q2 +10Q = 5.

(b) Demand

3P+Q2 +5Q−102 = 0,

and supply

P−2Q2 +3Q+71 = 0.

4. [Market Equilibrium IV]

Find the equilibrium price and quantity for the following related market for three goods.

Qd1 = 23−5P1 +P2 +P3 Qs1 =−8+6P1.

Qd2 = 15+P1 −3P2 +2P3 Qs2 =−11+3P2.

and

Qd3 = 19+P1 +2P2 −4P3 Qs3 =−5+3P3.

Submission deadline: October 10, 2018 on Canvas Page 2 of 3

Instructor: Ram Sewak Dubey ECON 317: Problem Set 3 October 4, 2018

5. [National Income I]

Given Y =C+ I +G+NX ,C =C0 +bY, I = I0,G = G0, and NX = NX0,

where C0 = 135, b = 0.8, I0 = 75 and G0 = 30, find the equilibrium national income and the aggregate household consumption C in equilibrium.

6. [National Income II]

Given

Y =C+ I +G+NX ,C =C0 +bYd, I = I0,G = G0, and NX = NX0,

where Yd = Y −T, and T = T0 + tY

and C0 = 85, b = 0.75, I0 = 30 and G = NX = 0, T0 = 20 and t = 0.20. Here T is the total amount of taxes the households have to pay with T0 being the fixed amount of taxes (regardless of income) and t is the tax rate (as a fraction of income Y ). Find the equilibrium national income, the aggregate household consumption C in equilibrium and the total amount of taxes paid by the households..

7. [National Income III]

Given

Y =C+ I +G+NX ,C =C0 +bYd, I = I0,G = G0, and NX = NX0,

where Yd = Y −T, and T = T0 + tY

and C0 = 140, b = 0.5, I0 = 35 and G = 20, NX = 0, T0 = 30 and t = 0.20. Here T is the total amount of taxes the households have to pay with T0 being the fixed amount of taxes (regardless of income) and t is the tax rate (as a fraction of income Y ). Find the equilibrium national income, the aggregate household consumption C in equilibrium and the total amount of taxes paid by the households.

Submission deadline: October 10, 2018 on Canvas Page 3 of 3