Question

Guthrie Medical has a total cost function TC(q) = 100 + 50q + 10q^2, so that the marginal cost is MC(q) = 50 +20q. The price of medical care is currently P=90.

What is the quantity that Guthrie Medical will choose to produce?

At that quantity, what is the average total and average variable cost for Guthrie? (Hint: ATC(q) = TC(q)/q)

Can Guthrie operate in that market in the long term? What about the short term?

Guthrie would like to know what the lowest break even long-term price is for them. How would you go about advising them on it based on the information you have in this problem?

Answer 1

Q	TC	MC	MR	TFC	TVC	ATC	AVC
0	100	50	90	100	0
1	160	70	90	100	60	160	60
2	240	90	90	100	140	120	70
3	340	110	90	100	240	113	80
4	460	130	90	100	360	115	90

1.
He would choose to produce Q= 2 as MC=MR

2. ATC = 120 and TC = 240

3. No he cannot operate in the long run as he would run into losses. But in short run he is able to cover the variable cost so he can run in short run.

4. Break even is where TR-TC= 0
The formula to calculate the breakeven pricing is,
= (Fixed cost/ no of desired units) + unit variable cost
= (100/2)+60 =110