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HW#4
(50 Points)
1. A profit maximizing competitive firm has a total cost function given by C(Q). Since
this firm is a polluter the government imposes a tax of $t per unit of output that the
firm produces.
(a) Write down the firms new total cost function.
(b) Write out the firms profit max. problem. Write out the corresponding first order
condition.
(c) Graph the firms' short run competitive equilibrium (price line ATC & MC curves)
before and after the tax on the same graph. (Assume that the firm is making
supernormal profits before and after the tax)
(d) Is the per unit tax effective in limiting quantity produced? Explain why or why
not.
2. A competitive firm has short-run total costs given by: C(Q) = 100 + 2Q +Q2
(a) If the competitive market price is $25 how much will the firm produce? (Use
calculus)
(b) Assuming the firm has the same cost curves in the long-run, how much will it
produce in the long run?
3. An industry is composed of 100 identical firms with total costs of the ith firm given
by C(Qi) = 2Qi2 +6Qi + 18.
(a)
What is the short run supply curve for the industry?
(b)
Given that market demand is Qd = 840 -2P find the equilibrium market
price and the profit of each firm at that price.
4. (a) Draw a graph of the firms TFC.
(b) Next assume that a lump-sum tax (a fixed amount independent of output level) is
imposed on this firm. Draw the new TFC.
(c) On a separate graph draw the firms short run ATC and AVC & MC curves before
and after the imposition of the tax.
(d) Can a lump-sum tax be used successfully to reduce output? If so draw a graph of
the short run cost curves to show how this may be accomplished.
5. Consider a competitive firm that can produce the same good in either of two plants
with cost functions C1(Q1) and C2(Q2) respectively. The firm produces Q1 units of the
good in the first plant and Q2 units of the good in the second plant. It sells a total of Q1 +
Q2 units. Write down the firms profit max problem and the corresponding first order
conditions. Interpret the meaning of the first-order conditions in words.