# 6.8) Indicate whether each of the following statements is true, false, oruncertain. Explain why.a.A proportional tax on all commodities including leisure is equivalent to a lump sum tax.b.Efficiency is maximized when all commodities are taxed at the same rate.c.Average cost pricing for a natural monopoly allows the enterprise to break even, but theoutcome is (most likely) inefficient

Question
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6.8) Indicate whether each of the following statements is true, false, or
uncertain. Explain why.
a.
A proportional tax on all commodities including leisure is equivalent to a lump sum tax.
b.
Efficiency is maximized when all commodities are taxed at the same rate.
c.
Average cost pricing for a natural monopoly allows the enterprise to break even, but the
outcome is (most likely) inefficient
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Step 1

To determine whether the statements are true or false.

Step 2
1. The given statement is true. A proportional tax on all commodities (including leisure) is equal to a lump sum tax. Suppose, initially the budget constraint is given as:

PcC + wL = I

Where Pc is the price of consumption good and w is the price of leisure. C and L denotes the quantities of consumption good and labor respectively. Income is denoted by ‘I’. Suppose government imposes a proportional tax on all commodities (including leisure). The new budget constraint is:

(1 – T) PcC + (1 – T) wL = I

PcC + wL = I’

Where I’ equals I/(1 – T) which is less than 1.

So, a proportional tax does not change the relative prices but reduces the income. So, it is like a lump sum tax.

Step 3

2. This statement is false because efficiency is not maximized when all the commodities are taxed at the same rate. Consider two commodities: milk and alcohol. There is a large proportion of population which purchase milk for their daily needs and there are some alcoholic individuals purchasing alcohol. Both the goods canno...

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