Doufffelberry Juice is a mild intoxicant. It is produced on farms where douffelberrys are grown. Baskets of Doufffelberries (B) are produced using grams of seeds (S) and hours of labour spent growing berries (L) , according to the production function
B = SL. The marginal product of L is MPL = S
4L and the marginal product of S
is MPS = L
4S.
Once the baskets of berries have been produced, they are squeezed to make litres of juice. The production function for juice is J = Min B, H , where J is litres of juice and H hours of labour spent squeezing berries. Both kinds of labour cost $9 per hour and seeds cost $9 per gram
a) How much B and H should be used to produce 10 litres of juice?
b) How much S and L should be used to produce 10 baskets of berries?
c) How much does it cost to produce 100 litres of juice?
d) Does the complete process exhibit constant, increasing or decreasing returns to scale? Hint: If you double all inputs (S, L and H) what happens to the output J?