Question

2. You are a wine blender. To make one bottle of red wine, you use 4 parts zinfandel, Z, and 1 part merlot, M. Zinfandel sells for $1 per part, P, = 1, and merlot sells for $2 per part, P = 2. Let stand for bottles of red wine. a. Find the production function for red wine. b. What is the total cost function for red wine? c. How much will it cost to produce 100 bottles of red wine?

Answer 1

Answer 2

(a)

It is given that in order to produce 1 bottle of wine it requires 4 parts of Z and 1 part of M. Thus he is producing Output Bottles using resources at a fixed proportion.

Thus production function is given by :

Q = min{Z , 4M}

where Q = Number of Bottles, Z = amount of zinfandel and M = Merlot.

(b)

Total Cost(C) = P_zZ + P_mM i.e. Z + 2M

Minimize : Z + 2M

subject to : min{Z , 4M} = Q

When we have function of the above form, In order to minimize such type of cost, a function hires that amount of M and Z such that kink of isoquant will occur and kink of isoquant for this function will occur when Z = 4M.

Hence we have min{Z , 4M} = Q => min{Z , Z} = Q => Z = Q and hence 4M = Z = Q => M = Q/4

Thus, Total Cost(C) = Z + 2M = Q + 2(Q/4) = 1.5Q -----------------Total Cost Function

(c)

Now we want Q = 100 => C = 1.5Q = 1.5*100 = 150.

Hence, Total cost of producing 100 bottles of red wine is 150