Question

Assume that the consumption function is given by C = 200 + 0.7(Y – T). Also assume that taxes are not fixed but described by the tax function: T = 100 + 0.2Y. The production function is Y = 50 K0.5 L0.5, where K = 100. If L increases from 100 to 144, then consumption increases by:

Answer 1

Answer:

Consumption has increased by 560

Explanation:

Since consumption function is given as:

$C = 200 + 0.7(Y - T)$

Tax function:

$T= 100 + 0.2Y$

Production function:

$Y= 50K^{0.5}L^{0.5}$

When K = 100, we have production function to be:

$Y= 50\times100^{0.5}L^{0.5}$

And that gives:

$Y= 50\times10L^{0.5}$

which is

$Y= 500L^{0.5}$

If you substitute Y in the tax function, we have:

$T= 100 + 0.2\times500L^{0.5}$

Which gives:

$T= 100 + 100L^{0.5}$

Now, putting substituting T and Y in consumption function, we have:

$C = 200 + 0.7(500L^{0.5} - 100 - 100L^{0.5})$

and this gives:

$C = 200 + 0.7(400L^{0.5} - 100)$

Now, when L = 100

$C = 200 + 0.7(400\times100^{0.5} - 100)$

We have

$C = 200 + 0.7(400\times10 - 100)$

which is

C = 2930

Therefore C = 2930 when L = 100

Also when L = 144

$C = 200 + 0.7(400\times144^{0.5} - 100)$

We have

$C = 200 + 0.7(400\times12 - 100)$

which is

C = 3490

Therefore C = 3490 when L = 144.

Hence, if L increases from 100 to 144

Then consumption increases by 3490 – 2930 = 560.

And that is the required answer.

Answer 2

Answer: Consumption has increased by 30800.

Explanation:

Given : consumption function C=200 +0.7 (Y-T)

       Tax function T= 100 + 0.2Y

       Then the production function Y=50K0.5L0.5

Thereafter they give us k=100 in both cases for L =100 and for L=144

K is capital and L stands for labour so we calculate how much does the consumption changes when labour (L) varies from 100 to 144.

Firstly we find production(Y), Tax (T) and the consumption(C) for labour (L) = 144 given k=100 so we substitute to the above given formulas.

Production for K=100 and L=44

Y= 50(100)0.5(144)0.5 then we compute on a calculator and get  

Y= 180000  

Then we find tax (T) for K=100 and L=144 as we have found Y the production at this level (Y= 180000) we use the above mentioned tax formula:

T = 100+ 0.2(180000)

T= 36100

After tax we can now compute the consumption at this level as now we have found the tax and production at K = 100 and L=144. Substitute tax (T) and production (Y) to the consumption function.

C1= 200 +0.7(180000-36100)

C1= 100930

Now we use the same method to find consumption at K=100 and L=100 so we can calculate the difference:  

Y=50 (100)0.5(100)0.5      , substitute K=100 and L=100 on the production function

Y= 125000

Then we calculate tax (T) for a production level of Y=125000

T=100 +0.2(125000)   substitute Y on the tax (T) function

T= 25100

Thereafter we find consumption( C) at a level of Labour(L) = 100 and capital(K)= 100

C2= 200+0.7(125000 – 25100)  substitute tax(T) and Production in the consumption(C) function.

C2=70130

Thereafter C1-C2 will be the change between the consumptions at level L=100 and L=144 where K=100 in both cases.

So Consumption (C) has increased by 100930-70130= 30800.