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Suppose that oil is perfectly divisible (you can buy non-integer quantities)
Suppose that oil is perfectly divisible (you can buy non-integer quantities). The marginal cost curve is given by MC=1.8Q+4MC=1.8Q+4. The demand curve is given by P=39−1.8QP=39−1.8Q, which gives MR=39−3.6QMR=39−3.6Q In the most efficient outcome (which perfectly competitive markets achieve), P=MCP=MC. Solve the equilibrium price and quantity in that case.
The most efficient equilibrium quantity is _____.
The most efficient equilibrium price is _____.
Now suppose that, for each unit of oil consumed, $5.84$5.84 worth of environmental damage is done. Solve the optimal Pigouvian tax (per unit) that would obtain the socially-efficient outcome where less oil is produced and sold. The optimal tax per unit is $_____.
Expert Solution
Given that;
MC=1.8Q+4P=39−1.8QMR=39−3.6QMC=1.8Q+4P=39−1.8QMR=39−3.6Q
Equate the demand equation with the marginal cost equation, and solve for the efficient output:
39−1.8Q=1.8Q+4Q=9.7239−1.8Q=1.8Q+4Q=9.72
The most efficient equilibrium quantity is 9.72 units.
Substituting the efficient output into the demand equation, we get price as:
P=39−1.8(9.72)P=$21.50P=39−1.8(9.72)P=$21.50
The most efficient equilibrium price is $21.50.
The Pigouvian tax is equal to the external cost (damage) caused by the negative externality. This will shift the marginal cost curve (private cost curve) upward and to the left, with an amount equal to external cost. The resultant curve is called social marginal cost (SMC):
MSC=MPC+EMSC=1.8Q+4+5.84SMC=1.8Q+9.84MSC=MPC+EMSC=1.8Q+4+5.84SMC=1.8Q+9.84
The socially efficient output occurs at the intersection of the SMC with the marginal benefit curve (MB), the demand curve:
SMC=MB1.8Q+9.84=39−1.8QQ=8.1P=$24.42SMC=MB1.8Q+9.84=39−1.8QQ=8.1P=$24.42
The socially efficient output and price are 8.1 units and $24.42, respectively. The per unit tax is calculated as:
Per unit tax=$5.848.1=$0.72
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