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Department of Agricultural and Resource Economics UC Davis ARE 100A Fall Quarter 2013 Problem Set 1 Due Date: Friday, October 4, 2013 1. Consider the...

consider the followwing equation of a linear demand curve:q1=a-bp1
a)show demand is unit-price elastic at the midpoint of the demand curve

Problem Set 1 Due Date: Friday, October 4, 2013 1. Consider the following demand function of an individual for good 1: 101 12 23 34 q pp pY ββ β β β = ++ + + Where 123 ,, ppp are the prices of good 1,2, and 3, respectively, and Y represents the income of the individual. Suppose good 1 and 2 are substitutes while good 1 and 3 are complements. (a) Describe in words what 1 β , 2 β , 3 β , and 4 β measure. (b) Can you say anything about the expected signs of 1 β , 2 β , 3 β , and 4 β in the demand equation? (c) Write out the formulae for the own price elasticity, cross price elasticities, and income elasticity of demand for good 1. 2. Now consider the following specific demand function for good 1 : 11 20 2 4 q pY = −+ (a) What are the price and income elasticities of demand when 1 3 p = , and 4 Y = ? (b) What are the price and income elasticities of demand if the demand function for good 1 is given by 12 1 2 q pY = 3. Consider the following equation of a linear demand curve: 11 q a bp = (a) Show demand is unit- price elastic at the midpoint of the demand curve. (b) Show demand is elastic above the midpoint of the demand curve. 4. Assume there are only two firms producing good 1. The inverse supply function of the first firm is given by 1 1 5 2 q p = while that of the second firm is 11 5 pq = (a) Derive the market supply curve. (b) Suppose there is only one consumer of the good whose demand curve is given by 11 20 2 qp = . What is firm 1’s and firm 2’s price elasticity of supply at the equilibrium price? 5. Suppose that the inverse demand curve of a good is given by 1 10 10 pq = and the supply curve is represented by 5 10 qp = . (a) Graph the supply and demand functions. 1
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(b) What is the equilibrium price and quantity? (c) Suppose that the government imposes a specific tax of 2 τ = on the producers. On a new graph, graph the pre-tax supply curve, the post-tax supply curve, and the demand curve. (d) What is the new equilibrium price and quantity with the tax in place? (e) How much tax revenue is raised by the government? (f) Compute the equilibrium price and quantity that would prevail if the specific tax was in fact imposed on consumers. Compare your answer with what you obtained in d. 6. Compute the incidence of a specific tax on consumers and producers if the demand and supply functions of a good are given by 0.3 1 2 qp = and 0.6 1 2 qp = 7. Consider the following demand equation : 11 34 2 qp = . The supply equation of the good is given by 11 10 2 qp = + . (a) What is the equilibrium price and quantity? (b) If the government imposes a price ceiling on the good at $5 , what is the effect on the quantity supplied and demanded? (c) If the government purchases the good at $7, how many units of the good will be produced? How many units of the good will consumers purchase? 2
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