Question

Sum the following marginal revenue schedules horizontally to derive a function in the form of MR = f(Q) and define the output ranges over which the summed function applies:

MR1 = 30 – 0.01Q1 and MR2 = 40 - 0.02Q2
MR = _________________
Q Range = _____________

Answer 1

ToTo sum the marginal revenue schedules horizontally, we first need to express both MR1 and MR2 in terms of the same output variable. Let's use Q as the common output variable. Since MR1 and MR2 are functions of Q1 and Q2 respectively, we can express Q as the sum of Q1 and Q2:

Q = Q1 + Q2

Now, solve for Q1 and Q2 in terms of Q:

Q1 = Q - Q2
Q2 = Q - Q1

Now, substitute these expressions for Q1 and Q2 in the MR1 and MR2 equations:

MR1 = 30 - 0.01(Q - Q2) = 30 - 0.01Q + 0.01Q2
MR2 = 40 - 0.02(Q - Q1) = 40 - 0.02Q + 0.02Q1

Now, sum MR1 and MR2 horizontally:

MR = MR1 + MR2 = (30 - 0.01Q + 0.01Q2) + (40 - 0.02Q + 0.02Q1)

Combine like terms:

MR = 70 - 0.03Q + 0.01Q2 + 0.02Q1

Since we don't have specific output ranges for Q1 and Q2, we can't define the exact output ranges for the summed function. However, the function we derived is applicable within the given output ranges for Q1 and Q2.