Econ302-hw4-summer09-1 - 1 Econ302 Homework Assignment 4...

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Econ302 Homework Assignment 4 Due Thursday June 11 (Questions 1, 2, and 3 will be graded) Name: 1. There are currently 100 identical firms in the perfectly competitive gadget manufacturing  industry, each having short-run total costs given by 2 0.5 10 5 STC q q = + + 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, S Q ? b. Suppose the market demand for gadgets is given by 1100 50 . D Q P = -   What is the  equilibrium price and quantity in this market? What will each firm’s total short-run  profits be? 1
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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. 2
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e. Suppose the government imposed a tax of $3 on each gadget sold. How would this tax  change the market equilibrium? 3
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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. 2.   Dayna’s   Doorstops,   Inc.   (DD),   is   a   monopolist   in   the   doorstop   industry.     Its   cost   is C = 100 - 5Q + Q 2 , and demand is P = 55 - 2Q.
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