There are currently 100 identical firms in the perfectly competitive gadget manufacturing industry, each having short-run total costs given by
STC= 0.5q^2 +10q +5
where q is the output of gadgets per day.
a. What is the short-run supply curve for each firm in the industry? What is the short-run supply curve for the industry as a whole,Qs?
b. Suppose the market demand for gadgets is given by
Qd = 1100-50p
What is the equilibrium price and quantity in this market? What will each firm's total short-run profits be?
c. Graph the market demand and supply curves and compute total producer surplus.
d. Show that the total producer surplus you calculated in part (c) is equal to total industry profits plus industry short-run fixed costs.
e. Suppose the government imposed a tax of $3 on each gadget sold. How would this tax change the market equilibrium?
f. How would the burden of this tax be shared between sellers and buyers of gadgets.
g. Calculate the total loss in producer surplus as a result of the tax on gadgets. Show that this loss equals the change in total short-run profits in the gadget manufacturing industry.