Week 44 Microeconomics Exercises

Question 1

One of the reasons why men have shorter lines at public rest rooms is because their bathroomshave many more urinals than toilets so turnover is much faster. The efficiency of urinals in termsof water usage and time savings seems clear, yet no one uses urinals in their own homes. Thisseems to be a curious puzzle. What reasons would an economist give to explain this puzzle?

The costs and benefits of having a urinal in your home must be different than the costs andbenefits in public places. For example, less benefit because there are no line-ups in your home(usually). Space is more scarce in the home.

Question 2

Suppose demand is P = 20− 3Qd and supply is P = 5 + 2Qs, what will prices be in equilibrium?What is the equilibrium quantity?

The equilibrium price is p∗ = 11 and the equilibrium quantity is Q∗ = 3.

Question 3

The supply function is: P = 10 + 5Q and the demand function is P = 26 − 3Q. Equilibriumprice and quantity is found by solving this system of equations: Q = 2 and P = 20

Question 4

Let supply be given by P = 4Qs and demand by P = 12− 2Qd. Suppose we now place a tax of 6per unit of output on the seller. What happens to supply and demand, and the quantity demandedat the equilibrium after the tax is imposed? What fraction of the per unit tax does the consumerpay?

After the tax is imposed supply contracts inward by the value of the tax, demand remains thesame. The quantity demanded falls from 2 to 1. The consumers pay 2

6 of the per unit tax.

1

Question 5

Suppose demand for seats at football games is P = 1900− 150Q

d and supply is fixed at Qs = 90000seats. Find the equilibrium price and quantity of seats for a football game using algebra. Supposethe government prohibits ticket scalping (selling tickets above their face value), and the face valueof tickets is fixed at $50. How much excess demand is there? Suppose the next game is a majorrivalry and so demand jumps to P = 2100 − 1

50Qd. Now, how much is excess demand?

Without a price ceiling the equilibrium quantity is 90,000 and the equilibrium price is $100.When the price ceiling is imposed excess demand is 2500 tickets. When demand is higher excessdemand increases to 12,500 tickets.

Question 6

Suppose demand is p = 8 − 2Qd and supply is Qs = 2p, where the quantities are in pounds perday and the prices are in $ per pound. How would the equilibrium price and quantity change if themarginal cost of every producer were to increase by $2 per pound?

The supply curve shifts inward after the increase in the marginal costs to p = 2 + 12Q

s Theequilibrium price increases from p∗ = 8

5 to p∗ = 165 and equilibrium quantity falls from Q∗ = 16

5 toQ∗ = 12

5

NOTE: Look at slide 57 from lecture 1 (in week 43) and page 39 in textbook, to see more onfactors that shift supply curves.

Question 7

If Pernille has rational preferences and she only consumes two goods, can both of them be infe-rior? Explain why or why not?

The definition of an inferior good is that the income effect is negative. A rational person alwaysspends all of her money, keeping in mind that there is no savings in this model.

If a rational consumer was spending all of her income on two inferior goods and income rose,then the quantity demanded of both goods would fall. This would mean that the consumer is notspending all of her income. Therefore, at least one good must be normal.

2