An economy is described by the following equations: = 2,600 + 0.8 ( Y – T ) – 10

Question

An economy is described by the following equations:

= 2,600 + 0.8 (Y – T) – 10,000r

= 1,800

= 100

= 3,150   

The real interest rate, expressed as a decimal, is 0.10 (that is, 10 percent).

a. Find a numerical equation relating planned aggregate expenditure to output.

Instruction:  Enter your response for mpc rounded to one decimal place.

PAE = ? +? Y.

b. Using a table (or algebra if you have used the appendix to this chapter), solve for short-run equilibrium output.     

Instructions: If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Leave no cells blank. You must enter 'zero' for the answer to grade correctly.

Output Y

Planned aggregate expenditure (PAE)

Y – PAE

9,500

9,600

9,700

9,800

9,900

10,000

10,100

10,200

Short-run equilibrium output: ? .

C

= 2,600 + 0.8 (Y – T) – 10,000r

I P = 2,000 – 10,000r G

= 1,800

NX

= 100

T

= 3,150   

Explanation / Answer

a. Planned aggregate expenditure equation is given as ;

AE (or Y) = C + I + G + NX.

Plugging in the values from the table, we get,

AE = 2600 + 0.8(Y - T) - 10,000r + (2000 - 10,000r) + 1800 + 100.

Also T = 3150, then

AE = 2600 + 0.8(Y - 3150) - 10,000r + (2000 - 10,000r) + 1800 + 100.

MPC = 0.8

[this is determined by the general equation of consumption function, C = a + bY, where a is autonomous part of consumption and b is the MPC which depends on the level of income].

b. Using algebra, we get,

Y = 2600 + 0.8(Y - 3150) - 10,000r + (2000 - 10,000r) + 1800 + 100

Also r = 0.10

Y = 2600 + 0.8(Y - 3150) - 10,000*0.10 + (2000 - 10,000*0.10) + 1800 + 100

Y = 4500 + 0.80Y - 2520 - 1000 + 2000 - 1000.

Y = 1980 + 0.8Y...............................equation i.

Y - 0.8Y = 1980

0.2Y = 1980

Y = $9900. This is the short run equilibrium output.

OR BY USING THE TABLE WE GET THE FOLLOWING VALUES, WHERE PAE = 1980 + 0.8Y (from equation i).

Again, Y - PAE is zero at 9900 level of output. Hence the answer by both methods is correct and same.

Y PAE Y-PAE 9500 9580 -80 9600 9660 -60 9700 9740 -40 9800 9820 -20 9900 9900 0 10000 9980 20 10100 10060 40 10200 10140 60

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.