Question

Suppose the economy of Protoss consists of three people: Fenix, Zeratul, and Tassadar. The following table shows their consumer spending at the given disposable income levels.

Disposable income (each person)	Fenix Consumption	Zeratul Consumption	Tassadar Consumption
$2000	$1500	$1400	$1600
$4000	$2000	$1800	$2200

a. Identify each individual’s consumption function, i.e., the mathematical equation that describes the individual’s consumption schedule given income. (3 points)

b. Draw the individuals’ consumption functions. Label the graph fully. (3 points)

c. Identify aggregate consumption function. Show the intermediate steps. (Hint: You need to add individual disposable income and consumption spending.) (2 points)

d. On a separate graph, draw the aggregate consumption function. (1 point)

e. Suppose everyone’s disposable income becomes $6000. Calculate the individual consumption (for each person) and aggregate consumption. (2 points)

Answer 1

Consumption function has following form:

C = a + bY where C: Total consumption, a: Autonomous consumption, b: MPC (= C / Y) and Y: Disposable income

(a)

(1) Fenix:

MPC = (2000 - 1500) / (4000 - 2000) = 500 / 2000 = 0.25

When Y = 2000, C = 1500

1500 = a + 0.25 x 2000

1500 = a + 500

a = 1000

C = 1000 + 0.25Y

(2) Zeratul

MPC = (1800 - 1400) / (4000 - 2000) = 400 / 2000 = 0.2

When Y = 2000, C = 1400

1400 = a + 0.2 x 2000

1400 = a + 400

a = 1000

C = 1000 + 0.2Y

(3) Tassadar

MPC = (2200 - 1600) / (4000 - 2000) = 600 / 2000 = 0.3

When Y = 2000, C = 1600

1600 = a + 0.3 x 2000

1600 = a + 600

a = 1000

C = 1000 + 0.3Y

(b)

(c)

When Total income = 2000 x 3 = 6000, C = 1500 + 1400 + 1600 = 4500

4500 = a + 6000b.........(1)

When Total income = 4000 x 3 = 12000, C = 2000 + 1800 + 2200 = 6000

6000 = a + 12000b.........(2)

(2) - (1) yields: 6000b = 1500

b = 0.25

a = 4500 - 6000b [From (1)] = 4500 - (6000 x 0.25) = 4500 - 1500 = 3000

C = 3000 + 0.25b

(d)

NOTE: As per Answering Policy, 1st 4 parts are answered.