Question

Question 1:

An automobile repair shop charges the competitive market price of $$16 per bike repaired. The firm's short-run total cost is given by STC(Q)=Q3/3STC(Q)=Q3/3.

What quantity should the firm produce if it wants to maximize its profit?

What is the maximized profit at the optimal level of quantity and the price of $$16 (( round to two decimal points ))?

Draw the shop's total revenue and total cost curves, and graph the total profit on the same diagram. Using your graph, label the point of profit-maximizing quantity and its profit level.

Suppose now the new price is P′P′. What is the profit-maximizing quantity as a function of P′P′. If the price increases by a factor of four ((i.e. price = 4P')), how much does the profit-maximizing quantity increase?

Answer 1

*Answer:

a)

Given

STC=Q3/3

Marginal Cost is given by

SMC=dSTC/dQ=3*(Q2)/3=Q2

To maximize the profits, a perfectly competitive firm sets its output level such that Price =Marginal cost

So,

Q2=16

Q=4

Firm should produce 4 units to maximize profit.

b)

Total Cost=TC=Q3/3=(4^3)/3=21.33

Total Revenue=TR=P*Q=16*4=64

Profit=TR-TC=64-21.33=$42.67

Maximum profit =Profit at optimal output=$42.67

c)

Q	Total Cost	Total Revenue	Profit
	TC=Q3/3	TR=16*Q	TR-TC
0	0.00	0.00	0.00
1	0.33	16.00	15.67
2	2.67	32.00	29.33
3	9.00	48.00	39.00
4	21.33	64.00	42.67
5	41.67	80.00	38.33
6	72.00	96.00	24.00
7	114.33	112.00	-2.33
8	170.67	128.00	-42.67

d)

We have calculated earlier that

SMC=Q2

To maximize the profits, a perfectly competitive firm sets its output level such that Price =Marginal cost

So,

Q2=P'

Q=P'1/2

Optimal output is given by

Q'=P'1/2

In case New Price=4P', optimal output is

Q'=(4P')1/2=2(P'1/2)

Optimal output is doubled.

*** Please please like this answer so that I can get a small benefit. Please support me. Thankyou**