Question

Question 2: The equation for a firm’s short-run total cost is STC = 10 + 5q + 0.1q2. Its short-run marginal cost is SMC = 5 + 0.2q. The market price is $25 per unit.

a. What is the firm’s maximum profit?

b. If all of the firm’s fixed costs are sunk, what is the equation for the firm’s short-run supply curve? explain

c. If all of the firm’s fixed costs are non-sunk, what is the equation for the firm’s short-run supply curve? explain

Answer 1

a. The profit is maximum at Q = 100, which is found by TR-TC = Profit

Q	STC	TR	Profit
0	10	0	-10
10	70	250	180
20	150	500	350
30	250	750	500
40	370	1000	630
50	510	1250	740
60	670	1500	830
70	850	1750	900
80	1050	2000	950
90	1270	2250	980
100	1510	2500	990
110	1770	2750	980
120	2050	3000	950
130	2350	3250	900
140	2670	3500	830
150	3010	3750	740
160	3370	4000	630
170	3750	4250	500

b.

If fixed costs are sunk costs, then minimum price to supply should be equal to minimum average non sunk costs then,
ANSC = AVC = (5q+0.1q^2)/q = 5+0.1q
ANSC would be at minimum when Q= 0, ANSC = 5
To find the price at which supply happens, we need to equate marginal cost with price
SMC = P
5+0.2q=P
25+q=5P
So, Short run supply curve is
Q=5P-25 for P>5
Q=0, for P<5

c.

If fixed costs are non-sunk costs, then short run average costs should be equal to minimum average non sunk costs then,
ANSC = SAC = (10+5q+0.1q^2)/q = (10/q+5+0.1q)
Minimum ANSC is at a point where ANSC = SMC
10/q+5+0.1q=5+0.2q
10/q=0.1q
100 =q^2
Q=10
Since, ANSC(20) = 0.5+5+2 = 7.5, Minimum P = 7.5

So short run supply equation is
Q=5P-25 for P>7.5
Q=0, for P<7.5