Globo Public Supply has $1,000,000 in assets.Its demand curve is: P = 206 - .20•Q and its total cost function is: TC = 20,000 + 6•Q where TC excludes the cost of capital.If Globo Public Supply is $\underline{\text{ UNREGULATED }}$ ,find Globo's optimal price.
A)$206
B)$106
C)$56
D)$6
E)$3

Question

Quizplus · Accepted Answer

To find the optimal price, we need to find the quantity where marginal revenue equals marginal cost.

First, let's rewrite the demand equation in terms of Q:

P = 206 - 0.20Q

We can rearrange this equation to solve for Q:

Q = (206 - P) / 0.20

Next, let's find the marginal revenue:

MR = (change in total revenue) / (change in quantity)

Since total revenue is just price times quantity, we can write:

TR = P * Q

Then, taking the derivative with respect to Q:

d(TR) / d(Q) = P

So our marginal revenue is simply equal to the price.

Now, let's find the marginal cost:

MC = (change in total cost) / (change in quantity)

We can find the change in total cost by taking the derivative of the total cost function:

d(TC) / d(Q) = 6

So our marginal cost is simply equal to 6.

Setting MR equal to MC:

P = 6

This is obviously not a feasible price, as it is below the variable cost of producing each unit. Therefore, Globo Public Supply should shut down in the short run.

In the long run, if the market is still unregulated and Globo Public Supply continues to operate, the optimal price would be where MR = MC and P is at least equal to the minimum average variable cost. From our calculations above, we know that MR = P = 6, so we need to find the quantity that corresponds to a minimum average variable cost.

Average variable cost (AVC) is equal to total variable cost (TVC) divided by quantity:

AVC = TVC / Q

Total variable cost is equal to total cost minus fixed cost:

TVC = TC - FC

So we can write the AVC equation as:

AVC = (TC - FC) / Q

Plug in the given total cost equation:

AVC = (20,000 + 6Q - FC) / Q

We don't know the value of fixed cost, but we can set up an inequality that tells us what it needs to be in order for the minimum AVC to be greater than or equal to 6:

20,000 + 6Q - FC >= 6Q

Simplifying:

20,000 - FC >= 0

So as long as fixed costs are at least $20,000, the minimum AVC will be greater than or equal to 6.

Since we don't know the value of fixed costs, we can't say for sure what the optimal price will be. But we do know that it will have to be greater than or equal to $106 (the price that corresponds to a quantity of 500, which is the quantity where MR = MC when P = $206).

Therefore, the best choice is B: $106.

Globo Public Supply Has $1,000,000 in Assets UNREGULATED ‾\underline{\text{ UNREGULATED }} UNREGULATED ​ ,Find Globo's Optimal Price

Globo Public Supply Has $1,000,000 in Assets $\underline{\text{ UNREGULATED }}$ ,Find Globo's Optimal Price