ECON 101 Tutorial: Week 4

Shane Murphys.murphy5@lancaster.ac.uk

Office Hours: Monday 3:00-4:00 – LUMS C86

Outline

• Roll Call• Problems• Discussion

Exercise 1A consumer preferences over x and y are described by the utility function u(x,y)=xy. a) Draw two indifference curves. One representing

all bundles providing utility 9 and one representing all bundles providing utility 16.

Exercise 1The government has decided that the free market price of tobacco is too low.b) Let the price of good x be 10 and that of good y 10. Let the

consumer’s income be 60. Calculate the consumer’s optimal consumption bundle and represent your solution graphically. Determine the consumer’s utility.

At optimum, the slope of the indifference curve = slope of the budget constraintMRS = Px/PyMRS = Mux/Muy = du/dx / du/dy = y/xSo we have y/x = 10/10 => x = y

Budget constraint is 10x + 10y = 60Since x = y, we can rewrite this as 10x + 10x = 60So x = 3, y = 3

Exercise 1c) Redraw the graph of part b). Let income increase

to 80. Depict the effect of this change in wealth on the graph. Calculate the new consumer’s optimal consumption bundle. Determine the consumer’s utility and compare with the one of part b.

Now the bc is 10x + 10y = 80So x = y = 4

Exercise 1d) Redraw the graph of part b. Keep income at its

initial level 60 and let the price of good x fall to 5. Depict on the graph this change in prices. Calculate the new consumer’s optimal consumption bundle. Determine the consumer’s utility. Finally, represent the income and substitution effects graphically. From the drawn income and substitution effects is good x normal or inferior?

Now y/x = 5/10 = ½The budget constraint is 5x + 10y = 60Solving we get x = 6, y = 3.

Chapter 5: Exercise 6A person who consumes wine and cheese gets a rise, so his income increases from 3000 to 4000. Use diagrams to show what happens if both wine and cheese are normal goods. Now show what happens if cheese is an inferior good.

1st figure shows the effect of an increase in income. The rise in income shifts the budget constraint out from BC1 to BC2. If both wine and cheese are normal goods, consumption of both increases. If cheese is an inferior good, the increase in income causes the consumption of cheese to decline, as shown in 2nd figure.

Chapter 6: Exercise 5A consumer has income of 30000 a year and divides this income between buying food and spending on leisure. The price of food is 15 and of leisure is 10. Draw the consumer’s BC and an IC to show an optimum. Assume that the price of food rises in three stages over the year in 10 increments while the price of leisure stays at 10. Draw new BCs and identify new optimums. Derive the demand curve for food.

Chapter 6: Exercise 5

DiscussionIn small groups, consider: Economic models optimize some function with some constraint. Design a study with a utility function and constraint where the study is not of consumption goods with prices.

Is utility real? Can it be seen in brain scans?