Question

1. Suppose marginal cost and average cost are given by the following expressions: MC(x)=3x^1/2, AC(x)=2x^1/2. What is the profit maximising quantity when p=$3?

2. Suppose marginal cost and average cost are given by the following expressions: MC(x)=3x^1/2, AC(x)=2x^1/2. What is the value pf the long-run break-even price?

3. For any given level of the price of output, the supply curve of a producer tells the producer the amount of output to produce in order to maximise profits.

a. True

b. False

Answer 1

1. Total revenue, TR = p*x = 3x
Profit maximizing quantity is determined where MR = MC
MR = d(TR)/dx = 3
So, MR = MC gives,
3 = 3x^1/2
So, x^1/2 = 3/3 = 1
So, x = 1² = 1
Thus, x = 1

2. Long run break even price is that where P = minimum of AC
d(AC)/dx = 2(1/2)x^(1/2)-1 = x^-1/2 = 0
So, x = 0
Thus, P = 2x^1/2 = 2(0)^1/2 = 0
So, long run break-even price is 0.

3. True
(Supply curve shows the profit maximizing quantity at any given price.)