Suppose that Laylita sells empanadas at a perfectly competit

Suppose that Laylita sells empanadas at a perfectly competitive farmers\' market and that her total cost of producing empanadas is TC(q) = 40 + 0.1q^2 - 1/5q where q is the total number of empanadas that she produces.

(a) What is the average total cost of producing empanadas as a function of the quantity of empanadas produced?

(b) At what quantity, q, is the average total cost of producing an empanada minimized? What is the value of the average total cost at q?

(c) The price of an empanada is $4.20. What quantity of empanadas should Laylita produce to maximize her prot? If she remains open, what is her economic prot or loss?

(d) Suppose that the price of an empanada falls to $3.00. What quantity of empanadas should Laylita produce to maximize her prot at this new price? If she remains open, what is her new prot or loss? (1/2 point)

Solution

TC = 40 + 0.1q² - 0.2q

a) ATC = TC/q = 40/q + 0.1q - 0.2

b) ATC is minimized when d(ATC)/dq = 0

-40/q² + 0.1 = 0

q = 20

ATC = 3.8

c) Profit is maximized when P = MC

P = 4.2 = MC

MC = d(TC)/dq = 0.2q - 0.2

q = 22

Profit = P x q - TC = 4.2 x 22 - (40 + 0.1 x 22² - 0.2 x 22)

Profit = 8.4

d)

Profit is maximized when P = MC

P = 3 = MC

MC = d(TC)/dq = 0.2q - 0.2

q = 16

Profit = P x q - TC = 3 x 16 - (40 + 0.1 x 22² - 0.2 x 22)

Loss= -14.4