Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

CHAP. 3] THE MEASUREMENT OF ELASTICITIES 61
(b)
In Fig. 3-18, S 1 ,S 2 , and S 3 are three alternative supply curves. S 0 1 ,S0 2 , and S0 3 are the new supply curves after
the imposition of a per-unit tax on producers. S 1 has zero elasticity, S 2 has unitary elasticity, and S 3 has infinite
elasticity. Thus, given the demand curve, the more elastic the supply curve, the higher the new equilibrium
price (after the imposition of the per-unit tax), and the greater the burden of the tax on consumers.
3.28 If the market demand for agricultural commodities is price-inelastic, would a bad harvest lead to an
increase or a decrease in the incomes of farmers as a group? Why?
A bad harvest is reflected in a decrease in supply (i.e., an upward shift in the market supply curve of agricultural
commodities). Given the market demand for agricultural commodities, this decrease in supply causes the equilibrium
price to rise. Since the demand is price-inelastic, the total receipts of farmers as a group increase. When
the demand for an agricultural commodity is price-inelastic, the same result can be achieved by reducing the
amount of land under cultivation for the commodity. This is done in some farm-aid programs.
3.29 With reference to Fig. 3-19, consider the following two farm-aid programs for wheat farmers. I. The
government sets the price of wheat at P 2 and purchases the resulting surplus of wheat at P 2 . II. The government
allows wheat to be sold at the equilibrium price of P 1 and grants each farmer a cash subsidy of
P 2 2 P 1 on each unit sold. Which of the two programs is more expensive to the government?
Fig. 3-19
Under both programs, the total receipts of wheat farmers as a group are the same (OP 2 times OB). The greater
the fraction of this total paid by the consumers of wheat, the smaller the cost to the government. If D w is elastic at
every point of arc AE, consumers’ expenditures on wheat would be greater under the second program, and so the
second program would cost less to the government. If D w is inelastic at every point of arc AE, consumers’ expenditures
on wheat would be greater under the first program, and so the first program would cost less to the government.
If D w has unitary elasticity at every point of arc AE, both programs would cost the same to the government.
The way the above figure is drawn, the first program would cost less to the government. (We assumed no storage
costs. We have also not considered what the government does with the surplus wheat and what is the effect of each
of the two programs on the welfare of consumers.)
PRICE ELASTICITY WITH CALCULUS
3.30 Find the price elasticity of demand (e) for the curvilinear demand function of the form Q ¼ aP -b
For this demand function, dQ/dP ¼ 2abP 2b21 so that
e ¼ abP b 1 P
¼ b, since aP b ¼ Q:
Q
Thus, the demand function given is a rectangular hyperbola with the constant price elasticity of demand equal
to 2b.