Question

Suppose Healthy Hospital is a for-profit hospital operating with significant market power. The weekly inverse market demand is P = 500 – 2Q where Q is the number of patient days and P is the price. The marginal and average costs are constant at $100 per patient day. a. Given this information, solve for the profit maximizing level of output for Healthy Hospital. b. What price will Healthy Hospital charge? c. What is the value of profits earned given your answers in parts a and b? d. Suppose Healthy Hospital is instead a non-profit, quantity/quality maximizing firm. What is the new equilibrium price and quantity? [Think about this one, and you can do it!]

Answer 1

1. Inverse market demand of the hospital: -

Marginal Cost = Average Cost = $100

Total Cost = Q*(Average Cost) = 100Q

Now the profit function of the firm: -

$8pqb+Oy18OwuKskxPYlgAAAABJRU5ErkJggg==$

Or,

Now maximizing profit(π) with respect to Q.

Or,

Or, $EDDdJD9LmXzxoAAAAASUVORK5CYII=$

Therefore, Profit maximizing level of output, Q = 100

2. Price that Healthy Hospital will charge: -

$AMLttjlsdLTCgAAAABJRU5ErkJggg==$

3. The profits earned by the hospital: -

4. As Healthy Hospital is now a non-profit, Quantity maximizing firm. So now profit, π = 0

Therefore,

Or,

Or,

Or, $xsA3Q0RqukBpkugAAAAASUVORK5CYII=$    [ ]

Or, $IT2lq4ryPKQAAAAASUVORK5CYII=$

Therefore, new equilibrium Quantity, Q = 200

And new equilibrium Price, P = 500 – 2*200 = $100