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OSU ECON 4001.03 - Sol1

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Homework 1 Solution1 Econ 4001.03, Fall 2013 Prof. Lixin Ye Homework 1 Solution 1. True or False, and explain. 1) Comparative statics examines how exogenous variables change as endogenous factors change. False. Comparative statics examines how endogenous variables change as exogenous factors change. 2) If positive analysis is based on a model, and not the real world, then it is typically irrelevant. False. As long as the model is abstract from complexities of the real world trying to capture the “essentials”, then the analysis based on that would be typically relevant. 3) The quantity of a good that consumers demand depends only on the price of the good. False. The quantity of a good demanded depends on many factors including: price, consumers’ incomes, and the price of related goods. 4) When the demand curve for a good is elastic, a one percent reduction in the price of the good will increase a consumer’s expenditure on the good. True. When a good has an elastic demand, a one percent decrease in the price will result in a greater than one percent increase in the quantity demanded. Thus the price multiplied by the quantity will increase when the price declines by one percent. Alternatively, let R be the consumer’s expenditure, then we have from the lecture: Thus when ,1Qpε<−, /0dR dp <, i.e., a reduction in the price will lead to an increase in the consumer’s expenditure (or the firm’s revenue). 2. Legislators argue that a minimum wage law is instituted to help poor people. Economists can attack the minimum wage law on two fronts. First, some argue that government should not help the poor. Second, some argue that minimum wage laws actually hurt the poor because it creates unemployment. Which argument is normative and which is positive? An opinion about the role of government is a normative statement. An observation about the impact of a law is a positive statement. ,(1 )QpdRQdpε= +2 3. Suppose the market demand curve for a product is given by 500 15 20dQ PI=−+ and the market supply curve is given by 25 10 10sQ PK=−+ −. Assume initially that 10I = and 5K=. 1) What are the equilibrium price and quantity in this market? Substituting 10I = and 5K=into the demand and supply curves and setting dsQQ= implies 500 15 200 25 10 5025 77531PPPP− + =−+ −== At $31P =, the equilibrium quantity is 235 units. 2) What are the endogenous variables and the exogenous variables in the equilibrium model above? Since I and K are taken as given in the model, they represent the exogenous variables. P and Q are determined by the model, so they represent the endogenous variables. 3) Suppose K suddenly increases to 20. How will this affect the market equilibrium calculated in part 1)? Substituting 10I = and 20K = into the demand and supply curves and setting dsQQ= implies 500 15 200 25 10 20025 92537PPPP− + =−+ −== At $37P =, the equilibrium quantity is 145 units. The equilibrium price rises by $6 and the equilibrium quantity falls by 90. 4. Suppose demand for good A is given by 500 10 2 0.70dA ABQ PP I=− ++ where AP is the price of good A, BP is the price of some other good B, and I is income. Assume that AP is currently $10, BP is currently $5, and I is currently $100. 1) What is the elasticity of demand for good A with respect to the price of good A at the current situation?3 ,1010 0.208480AAAAQPAAQPPQε∂= =−=−∂ 2) What is the cross-price elasticity of the demand for good A with respect to the price of good B at the current situation? ,52 0.021480ABABQPBAQPPQε∂= = =∂ 3) What is the income elasticity of demand for good A at the current situation? ,1000.70 0.146480AAQIAQIIQε∂= = =∂ 5. The demand for labor is given by L(w) =1000 -.5w, where w is the minimum wage. 1) Find the level of w that maximizes the total wage payment, wL(w). We maximize w(1000 - .5w), which occurs where the derivative is zero: 1000 - w = 0, which implies w=1000. 2) What is the wage-elasticity of labor demand at the maximizing minimum wage? At w=1000, L(w) =1000 -.5w=500. Thus the wage-elasticity of labor demand at this point is given by ,1000.5


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