Let the economy's production function be Y = f(N, K) where Y is real GDP, N...

 

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Let the economy's production function be Y = f(N, K) where Y is real GDP, N is the population (and labour) and K is the stock of capital. The first partial derivatives are positive: a²y a²y fN = :> 0, fk = > 0. The second partial derivatives fNN ƏY ƏN ƏY Ək ƏN² Ək² <0 and fkk = a²y > 0. ƏNƏK 0 are negative, but the cross-partial second derivative is positive: fNK 10 marks for Question 1 a. Make a graph with the population on the horizontal axis and real GDP on the vertical axis. Draw the relationship between real GDP and the population. Explain why it has the shape you have drawn. (4 marks) C. < b. Suppose this economy is in a Malthusian world. Show the Malthusian equilibrium. (1 mark) Now there is a war which reduces the stock of capital. Show the new Malthusian equilibrium. Explain how the economy got to the new equilibrium. (5 marks) Let the economy's production function be Y = f(N, K) where Y is real GDP, N is the population (and labour) and K is the stock of capital. The first partial derivatives are positive: a²y a²y fN = :> 0, fk = > 0. The second partial derivatives fNN ƏY ƏN ƏY Ək ƏN² Ək² <0 and fkk = a²y > 0. ƏNƏK 0 are negative, but the cross-partial second derivative is positive: fNK 10 marks for Question 1 a. Make a graph with the population on the horizontal axis and real GDP on the vertical axis. Draw the relationship between real GDP and the population. Explain why it has the shape you have drawn. (4 marks) C. < b. Suppose this economy is in a Malthusian world. Show the Malthusian equilibrium. (1 mark) Now there is a war which reduces the stock of capital. Show the new Malthusian equilibrium. Explain how the economy got to the new equilibrium. (5 marks)

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