Assume we can use the Malthusian model to describe the situation in Twilightia.

ID: 1179594 • Letter: A

Question

Assume we can use the Malthusian model to describe the situation in Twilightia. In

particular, the relationship between its income per capita (y) and the growth rate of the population

(Delta L) is given by equation:

Delta (Difference in) L = y - 100

L) is given

Suppose its output is produced using labor and capital according to equation

Y = (K)^1/2(L)^1/2.

Assume K = 1, 000,000.

(a). Draw a graph with y on the horizontal axis and Delta L on the vertical axis, showing the relationship

between income per capita and population growth in Twilightia.

(b). Derive the relationship between population (L) and income per capita (y). (Hint: remember that

y= Y/L.) Sketch this relationship on a graph with L on the vertical axis and y on the horizontal

axis.

(c). Use the equations you derived to compute the steady-state values of L and Y.

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