Question

6. You drive a taxi. If you use premium unleaded, your cab gets 25 miles to the gallon. If you use regular unleaded, you get 23 miles per gallon. Let P stand for a gallon of premium, and R stand for a gallon of regular. a. If output (Q) is measured in miles driven, write your production function in terms of the two gasoline inputs. b. In a normal month, you drive 2,300 miles. If regular sells for $1.05 per gallon and premium sells for $1.15, how many gallons of each should you use each month?

Answer 1

a) Production function is Q = 25P + 23R. This is because each gallon of P gives a mileage of 25 while each gallon of R gives a mileage of 23.

b) From production function we have MRTS = 25/23 = 1.087 while the slope of the budget line is PPremium/PRegular = 1.15/1.05 = 1.095

Now MRTS < PPremium/PRegular

This implies that regular unleaded is more productive and you should use only regular unleaded

In this way P = 0 and so we have

Q = 25*0 + 23R

2300 = 0 + 23R

This becomes R = 2300/23 = 100

You should use P = 0 and R = 100.