Triple C Ranch (TCR) grows corn.
The market supply for corn is Qs = -9 +4P Market demand is Qd = 40 – 3P.
TCR’s cost function is 26 + 2q + 0.1q2, where q is the output of corn in ears.
A. The cost function is given as 26+2q+.1q2, average cost formula is= total cost/quantity. Plugging in, we get
Average cost=(26+2q+.1q2)/q=26/q+2+.1q.
Marginal cost=d(total cost)/dq=2+.2q.
Average fixed cost function= 26/q.
They have been plotted below in a single graph.
Blue line is the average fixed cost function. Green is the average cost function. Red is the marginal cost function.
b. Market price of corn will be where supply=demand. So,
-9+4P=40-3P
7P=49
P=7.
c. Profit maximizing output would be where MC=MR. As derived in part A, MC=2+.2q.
Revenue= Price*Quantity=((Q-40)/3)*Q=Q2/3-40Q/3
MR=2Q/3-40/3.
Equating MR and MC
2Q/3-40/3=2+.2Q
2Q-40=6+.6Q
1.4Q=46
Q=32.86.
Triple C Ranch (TCR) grows corn. The market supply for corn is Qs = -9 +4P...
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