Riiiiiima
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Hello,

I've problems with solving these questions, does anyone know how to do them ? I'd be very thankful for any help. I'm not here saying,
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username3037548
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Where are the questions
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Riiiiiima
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Sorry, i didn't noticed that!

I've problems with solving these questions, does anyone know how to do them ? I'd be very thankful for any help.

I.F(K,L)=12√KL
II.F(K,L)=12√KL+2
III.F(K,L)= A^0.1*K^0,2*L^0,7
IV.F(K,L)= K^2+L
V.F(K,L)=4(K/L)^0.4

What are the returns to scale of functions I-V?

Calculate marginal productivity of capital and marginal productivity of labour for those functions?

Knowing, that initial (for year 1) capital per worker (p.c.) is k=2, depreciation rate δ=0.2, savings rate s=0.4 and the economy is characterised by production function V, calculate capital p.c., consumption p.c., investment p.c. and net change of capital p.c. for the first 5 years starting from the initial point.

Using parameters from point 3., calculate steady state for function V.

Now imagine an economy, that makes only toy cars (the price of a toy car is 10$). Production of this economy is illustrated by production function I. Let us now imagine, that in the state of equilibrium K=100 and L=900. Calculate real and nominal wages for the workers. Try to use analogous method to calculate real and nominal rents for capital owners.

How is the income from production of toy cars (like in point 5.) distributed among the group of capitalists and workers? Comment on it.

im trying to find any materials to help me for hours now.. any help will be very appreciated
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Detiri17
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I believe returns to scale is found by finding the degree of homogeneity of the function
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Detiri17
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Marginal products you differentiate with respect to capital and then labour respectively. For the middle bit read around Solow's growth theory I think, after that I'm stuck because it's not anything I've done before so I'd have to read around it
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username3037548
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omg I was expecting something like assess monetary policy or something.

What year of economics is that? 3rd year undergrad?
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Riiiiiima
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its first year in university of Warsaw.
Detiri17 thanks for the ideas.. ill try to solve them according to what you said.
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Detiri17
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Hey ozilll, the first 2 bits are first year maths for economics and then it goes into first/second year for Solow's long run growth theory, I haven't done any of the rest but it doesn't look to bad, I'm second year, tbf I'd be able to answer it better if it was monetary policy haha, hopefully the Solows stuff is right Riiiima but everything looks different from different universities
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The Financier
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Would second Detiri's suggestion that returns to scale is found by finding the degree of homogeneity of the function. To find the marginal product of labour/capital, simply take the partial differentiation of the function with respect to whichever factor of production you desire.

Second bit is indeed likely a Solow growth model question.

I haven't covered the last part either, but as you're discussing the proportion of the income given to labour and vice versa for owners of capital, you'll probably want to find MP_n which equals the real wage when a firm is maximising profits. Using that I think you can extract the overall income given to labour and hence its proportion compared to rent for owners of capital.
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