Consider the following simple model of health and income: y = (1/2) h + x h = 2 y /2 Here, h denotes the average health situation of a citizen, and y denotes real GDP per capita. The variable x > 0 denotes an exogenous productivity variable. 2.1. Find the equilibrium, i.e., solve for h(x) and y(x). 2.2. Interpret the results you find in 2.1. 2.3. Analyze the effects of a permanent increase in productivity mathematically. 2.4. Analyze the effects of a permanent increase in productivity graphically. 2.5. Interpret the results you find in 2.3 and 2.4.