ECON 101 Tutorial: Week 4. Shane Murphy [email protected] Office Hours: Monday 3:00-4:00 – LUMS C86. Outline. Roll Call Problems Discussion. Exercise 1. A consumer preferences over x and y are described by the utility function u( x,y )= xy .
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A consumer preferences over x and y are described by the utility function u(x,y)=xy.
The government has decided that the free market price of tobacco is too low.
At optimum, the slope of the indifference curve = slope of the budget constraint
MRS = Px/Py
MRS = Mux/Muy = du/dx / du/dy = y/x
So we have y/x = 10/10 => x = y
Budget constraint is 10x + 10y = 60
Since x = y, we can rewrite this as 10x + 10x = 60
So x = 3, y = 3
Now the bc is 10x + 10y = 80
So x = y = 4
Now y/x = 5/10 = ½
The budget constraint is 5x + 10y = 60
Solving we get x = 6, y = 3.
A 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.
A 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.
In 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?