Q4: 10 points] Consider a firm operating in a market where each unit of its prod
ID: 1134176 • Letter: Q
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Q4: 10 points] Consider a firm operating in a market where each unit of its product can be sold at the constant price of a E R++ Suppose the firm's cost of producing a quantity qe R++ is given by C(q)-,q2, where e R++. The firm can choose the quantity but cannot affect or . (a) Write and draw the profit function of the firm in the format fX Y where f(x)- (b) Find the "profit maximizing quantity." What kind of mathematical object is it? Express it in the proper mathematical format. Draw it and describe its key properties (those properties that we have discussed in the class). Once you recognize what kind of object it is, then you will know what is meant by its "key properties" (c) Find the profit obtained by the firm when it produces at its profit maximizing level. What kind of mathematical object is it? Describe its key properties.Explanation / Answer
Answer 4)
In perfect competition market, long run equilibrium would be where AC(average cost) is minimum.
TC = Y3/3 + 18
AC = TC/Y = Y2/3 + 18/Y
To find the minimum of AC, we need to differentiate it & put it equal to zero.
dAC/dY = 2/3*Y + 18*(-1)Y-2 = 0
Solving this will give us Y = 3 (Quantity for single firm).
Minimum AC = 32/3 + 18/3 = 9 (price)
Putting this P in the demand equation will give the market demand
so P = 2001 - 2Y
Y = 996(market demand)
No of firms = 996/3 = 332
(b) if $6 tax is on the seller,
In the short run, both consumers and producers will suffer from the tax imposed.In the long run, since the supply curve is completely elastic, the new tax will reduce only consumer surplus. Producer surplus will remain equal to zero, since there are no profits to be made. all the burden wpould be on the buyer so price will increase to 9+6= 15
now the market demand would be 15 = 2001 - 2Y, demand = 993.
(c) a monopolist will maximize his proft at a point where MC =MR
2001 - 4Y = c
4Y = 2001 - c
Y =(2001 - c)/4
so P = 2001 - 2Y
P = 2001 - (2001 -c)/2
P = 2001 - 1000.5 - 0.5c = 1000.5 - 0.5c
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