Homework 2 Econ 1101 44 Principles of Microeconomics Deniz Cicek Due Thursday Feb 28 2008 Note Type everything but graphs and calculations for full credit Completely label all graphs for full credit Homeworks may not be submitted electronically Problem 1 12 points Consider the perfectly competitive market for mechanical pencils a Sketch a demand supply diagram for the market for mechanical pencils Label the equilibrium price and quantity on your diagram b You study survey data and observe that if mechanical pencils cost 5 then 5 wooden pencils are demanded while if mechanical pencils cost 10 20 wooden pencils are demanded Calculate the Cross Price Elasticity of Demand for mechanical pencils and wooden pencils How are these two goods related c Suppose the price of wooden pencils decreases Draw the effects of this shift on your diagram from part a Label the new equilibrium price and quantity In a sentence or two explain why you changed your diagram in this manner Explicitly state what happened to equilibrium price and quantity Hint Remember demand shifters from chapter 4 Use the information from part b to determine the direction of the shift Problem 2 10 points Assume that a consumer s Income Elasticity of Demand for education is 0 1 a What does this value tell you about this good b Sketch a demand supply diagram for the market for education Label the equilibrium price and quantity on your diagram Suppose consumer s income increases Draw the effects of this shift on your diagram from above Label the new equilibrium price and quantity Explicitly state what happened to equilibrium price and quantity Problem 3 5 points Suppose you are offered free pizza and you can eat as much as you want What would be the marginal utility of the last pizza you eat Justify your answer 1 Problem 4 15 points The following table shows the utility of consumption of Pizza to Daniel Quantity Per month 0 1 2 3 4 5 6 Total Utility 0 25 45 60 70 75 75 a Calculate the marginal utility for each quantity consumed b Suppose price of pizza is 15 How many pizzas should Daniel consume this month c Derive and graph Daniel s demand for pizza Problem 5 12 points There are two consumers Ceyhun and Mario in the market for comic books Their demand functions are given by QCD p 12 p QMD p 15 3p QCD denotes Ceyhun s demand and QMD denotes Mario s demand a Graph the market demand for comic books First draw individual demand curves Then draw the market demand curve b Write down the market demand function Problem 6 6points Suppose Mike spends his income on two goods M M s and Reeses Draw the following budget lines on separate graphs Make sure to label them clearly For each budget set also indicate whether or not the bundle M Ms Reeses 4 5 is affordable a Pm 5 Pr 4 I 40 b Pm 2 Pr 4 I 40 c Pm 4 Pr 2 I 20 2 Problem 7 8 points Suppose the price of skateboards is 10 and the price of rollerblades is 5 a Draw the budget line for a consumer with an income of 100 putting skateboards on the x axis b What is the slope of the budget constraint c What happens when the price of rollerblades increases to 7 Graph it d What happens when income drops to 50 Graph it Problem 8 32 points An individual consumes two goods Shoes S and Gloves G The marginal utilities of Shoes and Gloves are as follows MU S 100 2 S MU G 200 8G Also PS 2 PG 4 and income I 100 a b c d e f g h Write the equation of the budget line Write the condition for optimality of the consumption bundle Solve for the consumer s optimal bundle of shoes and gloves Graphically drawing the budget constraint and our general indifference curves show the optimal consumption bundle Put shoes on the x axis Suppose price of gloves increases The new price is PG 8 Solve for the consumer s new optimal bundle of shoes and gloves On the same graph from part d show the new optimal consumption bundle Indicate what happens to the individual s demand for shoes and gloves after the price change Why does the demand for shoes change even though PS stays the same Now assume price of gloves does not change i e PG 4 but income decreases to I 50 Solve for the consumer s optimal bundle of shoes and gloves Show the optimal consumption bundle on a new graph 3
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