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a) Suppose that Y = AKalphaL1-alpha where
A is a measure of the level of technology called “total factor
productivity”. Assume that capital’s share 40% , output grows at
3%, capital grows at 2.5% and labour grows at 2%.

i) Calculate the growth of total factor productivity.

ii) What is another name for the growth of total factor
productivity?

The production function is given as Y = AK$\alpha$L1-$\alpha$

We can say it as, $\Delta$Y = $\Delta$A + $\alpha$$\Delta$K + (1-$\alpha$)$\Delta$L

Y = Total Output

A = Total Factor Productivity

K = Capital Input

L = Labor Input

%DY = %DA + $\alpha$·%DK + (1-$\alpha$)·%DN

.03 = $\Delta$A + (.025*.4) + (.02*.6)

Or, $\Delta$A = .03-.0122 = .02

Growth rate of total factor productivity is
2%

Can someone double check this solution please? and confirm the
correct answer so I would know if mine is correct.

Seems like 0.1 was used when the actual calculation was done in
line 1 instead of 0.01.(0.1 + 0.012 = 0.0122 instead of 0.01 +
0.012 = 0.022)

This is what I got when I calculated it:

0.03 = $\Delta$A + (0.025*0.4) + (0.02*0.6)

0.03 = $\Delta$A + 0.01 + 0.012

0.03 = $\Delta$A + 0.022

$\Delta$A = 0.03 – 0.022

$\Delta$A = 0.008

$\Delta$A = 0.08%

Can someone double check this solution please? and confirm the
correct answer so I would know if mine is correct.