Answer to Question #156162 in Microeconomics for Kacy

Question

Problem #1

1. Complete the following table and identify the quantity that maximizes profit.

Quantity TR MR TC MC

0 0 5

1 10 2

2 20 15

3 30 10

4 10 37

Problem #2

1. Suppose that each firm in a perfectly competitive market has a short-run total cost of TC = 75 + 500Q – 5Q2 + 0.5Q3, where MC = 500 – 10Q + 1.5Q2.

1. Calculate the output that minimizes the firm’s AVC.
2. What is the firm’s shutdown price?

Answer 1

Problem #1

Quantity TR MR TC MC Profit

0 0 5 -5

1 10 10 7 2 3

2 20 10 15 8 5

3 30 10 25 10 5

4 40 10 37 12 3

The quantities that maximizes profit are 2 and 3 with a maximum profit of 5

Problem #2

$AVC=(500Q-5Q^2+0.5Q^3)/Q$

$=500-5Q+0.05Q^2$

$AVC=MC$

$500-5Q+0.5Q^2=500-10Q+1.5Q^2$

$-5Q+10Q+0.5Q^2-1.5Q^2=0$

$5Q-Q^2=0$

$Q(5-Q)=0$

$Q=0$ and $Q=5$

Q = 5 minimizes the firms cost.

2.shut down price

find TC

$TC=75-50+Q – 5Q^2 + 0.5Q^3$

determine he shut down price by finding the minimum of the AVC

$=( 500Q – 5Q^2 + 0.5Q^3)/Q$

take the derivative of AVC and set them equal to zero and calculate

$(500-10Q+1.5Q^2)/Q-(500Q-5Q^2+1.5Q^3)/Q^2$

$Q=5$

evaluate AVC at Q=5

$500-5(5)+0.05(5)$

$=475.25$

shut down price =475.25