$9$ Kites are manufactured by identical firms. Each firm's long$-$run average and marginal costs of production are given by:

$AC=Q+\frac{100}{Q}$ and $MC=2Q$

where $Q$ is the number of kites produced.

a$.$ In long$-$run equilibrium, how many kites will each firm produce? Describe the long$-$run supply curve for kites.

b$.$ Suppose that the demand for kites is given by the formula:

$Q=8,000-50P$

where $Q$ is the quantity demanded and $P$ is the price. How many kites will be sold? How many firms will there be in the kite industry?

c$.$ Suppose that the demand for kites unexpectedly goes up to:

$Q=9,000-50P$

In the short run, it is impossible to manufacture any more kites than those already in existence. What will the price of kites be$?$ How much profit will each kitemaker earn?

d$.$ In the long run, what will the price of kites be$?$ How many new firms will enter the kite$-$making industry? How much profit will they earn?