Assignment:
Problems
1. Feasible Regions
State what types of returns to scale and marginal products each of the following functions exhibit: (assume X, Y 2 0)
(a) 23X0.3Y0.4
(b) 12X1.6Y0.5
(c) 2X0.4Y0.8
(d) 5X + 3XY - 4Y - 2Y2
2. Thought Problems
(a) A chemical plant uses heat to convert raw materials (A and B) into a product The reaction must take place at a certain high pressure, which is maintained by a spherical reaction chamber. What sorts of marginal products would you expect for each of the four resources (A, B. heat, and chamber size)? Note that for a sphere,
volume = (4/3)r3
surface area = 4r2
and (since pressure is independent of chamber size) the thickness of the chamber wall is also independent of size. What can you say about returns to scale in this process?
3. Vi-Tall Cereal
Tab Booleigh, chief cook at Health Foods Inc., makes Vi-Tal Cereal from rye and bran. Her recipe is as follows: 1 lb of Vi-Tall requires either i i/2 ibs of rye or Ib of bran. For batches of 10 lbs or more, spoilage reduces the output per unit of grain by 1/3. The prices per pound of rye and bran are $2 and $4 respectively A pound of Vi-Tall sells for $7.50.
(a) Does the production function define a convex, feasible region?
(b) Plot the isoquants for 4 and 12 lbs.
(c) What is the MRS of rye for bran?
(d) What are the MPs with respect to rye and bran?