Name: Econ 300 Final Exam all work for full credit. Answer all parts of question
ID: 1128544 • Letter: N
Question
Name: Econ 300 Final Exam all work for full credit. Answer all parts of questions. s of SUVs that consumers consider identical: 1.) Suppose there are two car frames and those built on truck frames. Anderson and Aufhammer (2013) estimated that each SUV is likely to inflict uncompensated harm to people other than its users, over its lifetime, of $12,000 if built on a car frame, and $20,000 if built on a truck frame, due to greater damage in crashes. There are 10 manufacturers of truck-based SUVs, and 10 manufacturers of car- based SUVs, and every firm has costs of weekly production, q, of C(q) = 10q2. Suppose the demand for SUVs per week in America is given by Qd=48,000-P. Currently, there is no special tax imposed on either type. a.) What are the competitive equilibrium price and quantity of SUVs? What is the total social welfare generated by the market for trucks? b.) What policy would move this market to its socially optimal production of car-based SUVs and truck-based SUVs? Find the welfare at this socially optimal point. How much has it risen from the welfare found in part (a,)Explanation / Answer
a) At the equilibrium, the quantity of production equals the demand.
Assume that all 10 car-based firms and 10 truck-based firms are identical
in production quantity (q) per week, price P and there is perfect competition.
So, the total production quantity is 20 q.
The total demand is Q = 48,000 - P = 20 q
Thus, we have P = 48,000 - 20 q
The marginal cost (MC) is the cost to produce one extra unit
MC = dC(q)/ dq = 20 q
The marginal revenue (MR) is P in a perfect competition.
At equilibrium, MC = MR
Therefore, 20 q = P
Therefore, 20 q = 48,000 - 20 q
Therefore, q = 1,200 is the production per week of each firm.
The total demand in America is 20 q = 24,000.
The production cost of each firm is 10 . sqr(q)
So, the production cost of 10 firms is 100 sqr(q) = 100 . sqr. (1,200) = 144,000,000
The price is P = 48,000 - 20 q = 48,000 - 20 (1,200) = 24,000
So, the total price of 12,000 units is 12,000 (24,000) = 288,000,000
However, each truck-based SUV inflicts damages worth 20,000
Since there are 12,000 such units, the total damages are 240,000,000.
Hence, the total social welfare = profit - social damages
= total revenue - total cost - social damages
= 288,000,000 - 144,000,000 - 240,000,000
= - 96,000,000
That is, effectively, truck-based SUVs reduce social welfare by 96 million.
b) The move that would move the market to optimal production is
to inculcate the environmental / social compensation into the selling price of the vehicle.
Then, P(car-based) = 24,000 + 12,000 = 36,000 and P(truck-based) = 24,000 + 20,000 = 44,000
In this case, in the absence of any limitation on production capacity, consumers will prefer
only car-based due to its price advantage.
Only the 10 car-based firms will function and will produce output 10 q.
The new price will be Padj = P + 12,000 for cars
Q = 48,000 - Padj = 10 qadj (so that the production matches demand)
So, Padj = 48,000 - 10qadj
Marginal Cost (MC) = dC(qadj)/ dqadj = 20 qadj
Marginal Revenue (MR) = Padj
since MC = MR at equilibrium
so, 20 qadj = Padj = 48,000 - 10 qadj
so, 20 qadj = 48,000 - 10 qadj
this gives qadj = 1,600 is the output of 1 firm
The total demand in America is 10 qadj = 16,000
The production cost of each firm is 10 . sqr(qadj)
So, the cost of 10 firms is 10 . 10 . sqr(qadj) = 100 . sqr(1,600) = 256,000,000
The adjusted price is Padj = 48,000 - 10 qadj = 48,000 - 10 (1,600)
Padj = 32,000
The total revenue is 16,000 (32,000) = 512,000,000
Now, we don't have to consider the damages separately since we have already accounted for them.
Thus, the social welfare is total revenue - total cost
Social welfare (after policy adjustment) = 512,000,000 - 256,000,000 = 256,000,000
Social welfare increases by 256 million.
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