Suppose that Px = A LX times W + A kx times r = 60 times r = 60 times W +40 time

Question

Suppose that Px = ALX times W + Akx times r = 60 times r = 60 times W +40 times r and that

Py = ALy times W + Aky times r = 75 times W +25 times r

A.) If Px = Py = 100, what are the equilibrium values for the wage rate and the rental rate?

B.)If Py increased to 120 and the input coefficients didnt change, wha would be the new equilibrium values of w and r?

C.) After the change in part B, would workers' wages buy more of less good X? More or less good Y? Would capital-owners' rent buy more or less good X? More or less good Y? Have real wages risenor fallen? The real rental rate?

D)Which trade theorem is your answer to part C an example of?

Thanks for help! :)

Explanation / Answer

a)
100=60w+40r
100=75w+25r

r=1
w=1

b)
100=60w+40r
120=75w+25r

r=1/5=0.2
w=23/15%u22481.53(3)

c)
Formally per-worker wage has increased for +53% ; Px remains the same but Py increased for +20%, thus depending on relative changes in level of employment:
aLX=60 %u21D2 L(x)=60/aX
aLY=75 %u21D2 L(y)=75/aY
L = L(x)+L(y) = 60/aX + 75/aY
Also depending on consumption/saving behavior
And type of the good (assuming normal) quantity demanded for both goods (X and Y) might increase.

But employed worker wage purchasing power increased for both goods X&Y.

Rent rate fell for -80%, thus for each employed unit of capital rent income purchasing power fell for both goods X&Y and for good Y rent purchasing power fell even more because of increase in price for good Y.

Depending on weight of goods X&Y in economy (assuming fixed weights 50% vs 50% with fixed quantities) price level increased for +10% but wage increased for +53%, thus real wage increased for:
(1.53/1.1)-1 = 46/33 - 1 = 13/33 %u2248 0.39(39) %u2248 +39.4%

Taking the same assumptions as above - real rental rate decreased for:
(0.2/1.1) - 1 = -9/11 %u2248 -0.81(81) %u2248 -81.2%

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