Output, Y , is produced according to a Cobb-Douglas production function, Y = AK^ L^1

where A is productivity, K is capital, and L is labor.

1. Show that, if K is fixed, then GDP per-capita is decreasing in labor.

2. Assume that the subsistence level is some y bar. Solve for the long-run population level in the Malthusian model, L* , as a function of A, K, and y bar.

3. Assume that = 0.3. If productivity, A, increases by 1%, by how much does long-run population (L*) increase? What is the percentage change in GDP per-capita?

4. Assume that subsistence requirements decline by 1%. What is the percentage change in population, L*? What is the percentage change in GDP per-capita?