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ID: 1146962 • Letter: B
Question
B 1 u.de x,x' A.ay . .RO adbceDc AaBbccDc AaBb AaBbC AaBbC AaBbC Heading 2 ts- o. a. Normal.No Spee. Headng 1 Tate Subtitle Font Paragraph Styles Problem 3, use the same demand function as Problem 2 . D (p. I, g) = 100-10p + 21-8gl with 1-3 and g-3. Use the supply function below. s(p) = 10 + 14p. Part A. Define the excess demand function X(p). What is the excess demand at p 2.50? What about p these results. Part B. Find the equilibrium price and quantity. What is the excess demand at that price? Part C. What are the price elasticities of demand and supply at that price? Part D. Now suppose the government imposes a tax t = 0.25 on suppliers of tape. Find the new equilibrium price and quantity, the effective prices to consumers and producers, and the total tax revenue collected.. Part E. What fraction of the tax is paid by consumers? (Hint: Compare the new effective price for consumers to the original price.) Verify that this fraction is equaltoe origina/ (pre-tax) price. How should we Es-Ep interpret the relationship between tax incidence (fraction of tax effectively paid by each side) and elasticity?.Explanation / Answer
Plugging in given values, Demand function: D(p) = 100 - 10p + (2 x 3) - (8 x 3)
D(p) = 100 - 10p + 6 - 24
D(p) = 82 - 10p
S(p) = 10 + 14p
(Part A) Excess demand: E(p) = D(p) - S(p)
E(p) = 82 - 10p - 10 - 14p
E(p) = 72 - 24p
When p = 2.5, E(p) = 72 - (24 x 2.5) = 72 - 60 = 12
When p = 4, E(p) = 72 - (24 x 4) = 72 - 96 = - 24
This means that when p = 2.5, quantity demanded exceeds quantity supplied, causing a shortage, but when p = 4, quantity supplied exceeds quantity demanded, causing a surplus. Therefore equilibrium price lies between 2.5 and 4.
(Part B) In equilibrium, D(p) = S(p)
82 - 10p = 10 + 14p
24p = 72
p = 3
Quantity = 10 + (14 x 3) = 10 + 42 = 52
In equilibrium, excess demand is zero because D(p) = S(p).
(Part C)
Elasticity of demand, Ed = ([dD(p) / dp] x [p / D(p)] = -10 x (3 / 52) = - 0.58
Elasticity of supply, Es = ([dS(p) / dp] x [p / S(p)] = 14 x (3 / 52) = 0.81
(Part D) With t = 0.25, new supply function becomes
S(p) = 10 + (1 - 0.25) x 14p
S(p) = 10 + 0.75 x 14p
S(p) = 10 + 10.5p
Equating with demand,
82 - 10p = 10 + 10.5p
20.5p = 72
p = 3.51 [Price paid by buyers]
Price received by sellers = 3.51 x 0.75 = 2.63
Unit tax = 3.51 - 2.63 = 0.88
Quantity = 82 - (10 x 3.51) = 82 - 35.1 = 46.9
Tax revenue = 0.88 x 46.9 = 41.27
NOTE: As per Chegg answering guideline, first 4 parts are answered.
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