Find (1) marginal and (2)the average functions for the following total function. Evaluate them at Q=3 and Q=5
π=q^2+13q+78
262
62
To find the marginal and average functions for the given total function π = q^2 + 13q + 78, we need to differentiate the total function with respect to q.
(1) Marginal function:
To find the marginal function, we differentiate the total function with respect to q. The derivative gives us the marginal function.
dπ/dq = 2q + 13
The marginal function is given by:
MC = 2q + 13
(2) Average function:
To find the average function, we divide the total function by the quantity q.
AVC = π/q = (q^2 + 13q + 78)/q = q + 13 + 78/q
Now, we can evaluate the marginal and average functions at Q = 3 and Q = 5.
1. Marginal function:
MC = 2q + 13
At Q = 3:
MC(Q=3) = 2(3) + 13 = 6 + 13 = 19
At Q = 5:
MC(Q=5) = 2(5) + 13 = 10 + 13 = 23
2. Average function:
AVC = q + 13 + 78/q
At Q = 3:
AVC(Q=3) = 3 + 13 + (78/3) = 3 + 13 + 26 = 42
At Q = 5:
AVC(Q=5) = 5 + 13 + (78/5) = 5 + 13 + 15.6 = 33.6