3. A Malthus Model (20 pts) Suppose population growth is given by the equation: Pt+1 (1 + g(Y//P))P = with g(Y+/P+) = Y+/P C. Production is a Cobb-Douglas production function of the form: Y = TP41-a where T is land, P is population, and Y is food production. a represents the impor- tance of population and land in production, and is generally between 0 and 1. Typically a problem set like this would be done writing on paper, and you would sub- mit a hard copy with your writing. Because of the current pandemic, all submissions are on Canvas, and so you'll have to type out the math in the assignment (though I'd recommend doing it by hand first and then typing it up once you have the solution). You have three options: (i) Take a screenshot of the math in your notes and include it into your file; (ii) Use the equation mode in Word (click on the Insert tab and then click on the Equation button; (iii) Use ^9 to denote exponents and _ to denote subscripts. (a) (10 pts) Find food per person Y/P. (b) (10 pts) What population P leads to zero population growth