As chief economist for Western Motors, your job is to figure out where to locate a new plant. The only inputs used in making automobiles are steel and labour, and the production function is A = SL. The marginal products of steel and labour
are MPs = L
4S and MPL = S
4L . You can locate the plant in Calgary,
where steel cost $7 per tonne and labour cost $7 per hour, or in Edmonton, where steel cost $8 per tonne and labour costs $6 per hour.
a) Will the plant exhibit constant, increasing or decreasing returns to scale in its production? Why?
b) prepare the cost of production, C, as a function of A for each of the two locations.
c) In which city should you locate the plant to minimize your cost per unit of output?