The given utility function is U= 100 Qt 0.5 Qc 0.5, the individual’s dual proble

Question

The given utility function is U= 100 Qt 0.5 Qc 0.5, the individual’s dual problem is to minimize E=Pt Qt +Pc Qc (show all the works and steps)

Where: Pt is the price of tea; P2 is the price of cake; Qt is the amount of tea; Q2 is the amount of cake; E is the total budget.

a. What is the minimum expenditure function?

b. If the Pt = 0.25 and Pc =1 and U= 2, what does the expenditure functions looks like?

c. What is the compensated demand function for Qt?

d. What is income elasticity for good Qt?

e. What is own price elasticity for good Qt?

f. What is the Engel curve?

Explanation / Answer

Engel curve describes how household expenditure on a particular good or service varies with household income.There are two varieties of Engel curves. Budget share Engel curves describe how the proportion of household income spent on a good varies with income. Alternatively, Engel curves can also describe how real expenditure varies with household income. They are named after the German statistician Ernst Engel (1821–1896), who was the first to investigate this relationship between goods expenditure and income systematically in 1857. The best-known single result from the article is Engel's law which states that the poorer a family is, the larger the budget share it spends on nourishment.

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