12. When prices are (P1, P2)= (1,2), the consumer demands (X1, X2) = (1,2). When prices are (Q1, Q2) = (2,1), the consumer demands (Y1, Y2) = (2,1). Is this consumer behaviour consistent with Weak Axiom of revealed preference ?

13. Prove that elasticity of demand is not constant along a linear demand curve.

14. Prove that expenditure share weighted sum of income elasticities equal 1.

15. Prove that both goods cannot be superior or inferior at the same time.

16. Relate elasticity of demand with different slopes of the demand curve.

17. The equation to the Engel's curve of a commodity is X = 50+2M2. Calculate the income elasticity of demand at M=$100. What can you infer about the nature of the commodity.

18. Calculate the own price elasticity of demand for the demand curve P= 15-3X at prices and compare the outcomes.

a) P=0

b) P=1/8

c) P=3

d) P=15

5. Lord Peter Pommy is a distinguished criminologist, schooled in the latest techniques of forensic preferences. Lord Peter is investigating the disappearance of Sir Cerdic Pichbot- tom who abandon his aging mother on a street corner in Liverpool and has not yet been seen since. Lord Peter has learned tat Sir Cerdic left England and is living under an assumed name some where in the Empire. There are three suspects, McAfee of Brass Monkey, Ontario, Canada, Manning of North Shag, New Zeland, and Stevenson of Gooey Shoes, Falkland Islands. Lord Peter has obtained Sir Cerdic's diary, which recorded his consump- tion habits in minute detail. By careful observation, he has also discovered the consumption behavior of McAfee, Manning and Stevenson. All three of these gentlemen, like Sir Cerdic, spend their entire income on beer and sausage. Their dossier reveal the following: . Sir Cerdic Pinchbottom - In the year before his departure, Sir Cerdic consumed 10 kilograms of sausage and 20 liters of beer per week. At that time, beer cost 1 English pound per liter and sausage cost 1 English pound per kilogram.(a) (b) McAfee McAfee is known to consume 5 liters of beer and 20 kilograms of sausage. In Brass Monkey, Ontario beer costs 1 Canadian dollar per liter and sausage costs 2 Canadian dollars per kilogram. Manning Manning consumes 5 kilograms of sausage and 10 liters of beer per week. In North Shag, a liter of beer costs 2 New Zeland dollars and sausage costs 2 New Zeland dollar per kilogram. Stevenson Stevenson consumes 5 kilograms of sausage and 30 liters of beer per week. In Gooey Shoes, a liter of beer costs 10 Falkland Island pounds and sausage costs 20 Falkland Island pounds per kilogram. Draw the budget line for each of the three fugitives, using a different color of ink for each one. Label the consumption bundle that each chooses. On this graph, superimpose Sir Cerdic's budget line and the bundle he chooses. After pondering the dossiers for a few moments, Lord Peter announced: "Unless Sir Cerdic has changed his tastes, I can eliminate one of the suspects. Revealed preferences tell me that one of the suspects is innocent." Which one? After thinking a bit longer, Lord Peter announced: "If Sir Cerdic left voluntarily, then he would have to be better off than he was before. Therefore is Sir Cerdic left voluntarily and if he has not changed his tastes, he must be living in