Patriots Inc. is a price-taking firm that produces Tricorns. Its short run cost
ID: 1202943 • Letter: P
Question
Patriots Inc. is a price-taking firm that produces Tricorns. Its short run cost function is c(y) = 5 + (y3)3 30 . a) Derive the following functions for Patriots Inc.: i) fixed cost ii) variable cost iii) average total cost iv) average fixed cost 1 v) average variable cost vi) marginal cost b) Graph these functions on a graph with y on the x-axis and dollars on the y-axis. c) Suppose the market price for Tricorns is $10. How many Tricorns should Patriots Inc. produce to maximize profits? How much will it earn in profits?
Explanation / Answer
Check if I am using the Right cost function . If it is wrong then write the correct cost function in the comments , I'ill revert back to you with the right answers in comments.
c(y) = 5 + (y3)3 + 30
i. Fixed Cost = C(0) = 26
ii. variable cost = 3Y
iii. average total cost = c(Y)/Y = 26/Y + 3
iv) average fixed cost = TC/Y = 26/Y
v.) average variable cost = VC/Y = 3
vi) marginal cost = dC(Y)/dY = 3
c.
Profit will be maximized at
MR = MC
So, Q = 3.33
TR = 10*3.33 = 33
Cost = 3*3.33
Profit = 23