nakota2k said:
Homework Statement
Your weekly cost to manufacture x bicycles and y tricycles is
C(x,y)=20,000+60x+20y+50√(xy)
a. What is marginal cost of manufacturing a bicycle.
b. What is the marginal cost of manufacturing a tricycle.
c. What is the marginal cost of manufacturing a bicycle at a level of 10 bicycles and 10 tricycles?
d. What is the marginal cost of manufacturing a tricycle at a level of 8 bicycles and 8 tricycles?
Homework Equations
The Attempt at a Solution
Normally I thought I would derive then plug in for x to get marginal cost.
I derived x and got (25y^1/2)/x^(1/2) +60 but I don't know what to do next or if that is even right.
I derived y and got (25x^1/2)/(y^1/2) +20 again I don't know what to do next
Yes, that is (roughly) what is meant by marginal cost.
For (a) and (b) that is all you can do, since a base pair (x,y) is not specified. However, in parts (c) and (d) you are given x and y values to work with. So, what do you think you should do next?
In principle, the true marginal cost of 1 bicycle, starting from a base of ##(x_0,y_0)##, would be
[tex]\text{actual marginal cost } = C(x_0+1,y_0) - C(x_0,y_0)[/tex]
For a cost function that does not "curve" too much (or for values of ##x_0## and ##y_0## that are not "too small" we have a reasonable approximation if we take
[tex]C(x_0+1,y_0) - C(x_0,y_0) \approx \frac{\partial C(x_0,y_0)}{\partial x},[/tex]
so that is why I said "roughly" before. Basically, the partial derivative is what economists often use. To be absolutely sure of your usage, check the definitions in your textbook or course notes.