Malthus Model 4) We will set up the Malthusian model that we covered in class. 5) 6) a) b) 8) Write down and graph the population growth rate 11 as a function of income per capita y. As in class, you can simplify the relationship to a linear function. Is the function increasing or decreasing? Write down and graph the income per capita y as a function of labour L. As in class, you can simplify the relationship to a linear flmction. Is the function increasing or decreasing? Combine the two graphs from a) and b) as we did in class. Make sure to have y on your xaxis for both graphs. Find and draw in the steady state levels of y and L. Now assume things change. Assume that you start of in the steady state (LSSLVSS). A natural disaster kills half of the population. Your labour force will therefore drop to half of your steady state labour force LES/2. Make a diagram to illustrate your answers. a) b) C) What does that imply for income per capita y, will it increase or decrease? Show this in your diagram. Aer income per capita adjusted also the population growth rate 11 will change. Will it increase or decrease? Show this in your diagram. What does your result from b) imply for your labour force L, will it increase, decrease or stay the same? Show this in your diagram. What will happen next? Ifthe dynamic keeps going. At some point a steady state will be reached. How does that steady state look like? Is it the same we had before or is it different? If it is different, how is it different? Summarize the short term effect and the long term effect of this dynamic on L, y, and n. Was the dynamic described a \"movement along the line\" or a \"movement of the line\"? Now assume things change. Assume that you start of in the steady state (55355). Technological change increases the productivity of labour. For the same amount of labour you can now produce more output. Make a diagram to illustrate your answers. a) The increased output for the same amount of labour implies that the relationship between L and y has changed systematically. Remember from 4b) how you represented the relationship between the two variables. If that relationship changes what has to change in your graph? Is this a \"movement along the line\" or a \"movement of the line\"? Your labour force does not change immediately, but we will have a higher level of income. Show this in your diagram. How will the population growth rate respond to the increase in income? Show this in your diagram. What does that mean for your labour force, will it increase, decrease or stay the same. Show this in your diagram. What will happen next? Ifthe dynamic keeps going. At some point a steady state will be reached. How does that steady state look like? Is it the same we had before or is it different? If it is different, how is it different? Summarize the short term effect and the long term effect of this dynamic on L, y, and n. Was the dynamic described a \"movement along the line\" or a \"movement of the line\