Question

A)

 Suppose the following graph shows the demand for, and supply of, apartments in New York City.

 Use the black point (plus symbol) to indicate the equilibrium monthly rent and quantity of apartments in the absence of price controls. Then use the green point (triangle symbol) to fill the area representing consumers' surplus, and use the purple point (diamond symbol) to fill the area representing producers' surplus.

B)

 Suppose that the government decides to impose a rent control of $1,900 per month on rental apartments in New York City. On the following graph, use the green point (triangle symbol) to shade the area representing consumers' surplus in the presence of rent control. Use the purple point (diamond symbol) to shade the area representing producers' surplus after the rent control. Then use the grey point (star symbol) to shade the area representing deadweight loss resulting from the rent control.

C)  In the presence of the rent control, consumers’ surplus increased/decreased by 400/320/240/80 million per month and producers’ surplus increased/decreased by 320/300/280/240 million  per month. The price ceiling on rent causes 960/480/320/160 million  per month of deadweight loss.

D)

 Which of the following are generally true of rent control? Check all that apply.

•  Non-price methods of rationing emerge.

•  All consumers gain from rent control.

•  The quantity of available rental apartments increases.

•  The quality of rental apartments improves.

•  People most in need of an apartment may not be able to rent one.

Answer 1

Solution:

A) Consumer surplus is the gain received by all consumers together, purchasing the good in question, here apartments. Similarly, producer surplus is the gain received by all producers together who sell the apartments. Since, demand curve plots all points telling the maximum willingness to pay by consumers, thus all area under a demand curve (above the price paid) represents the consumer surplus. In similar way, since, supply curve plots all points telling the minimum willingness to receive by sellers, thus all area above a supply curve (below the price received (equaling the price paid by consumers)) represent producer surplus.

In the below figure, equilibrium price is $2100 per apartment and equilibrium quantity is 1.6 millions of apartments in a month. Correspondingly, the green triangle gives the consumer surplus and purple triangle gives the producer surplus.

B) With rent ceiling of $1900, quantity demanded increases but the quantity sellers are willing to supply is very low, at this low rent (or low price). Thus, now the quantity in economy = 0.8 million apartments in a month. Due to such high demand and low supply at the rent ceiling (due to a binding rent ceiling), there is an excess demand for the apartments in NY, creating shortage of them. Thus, dead weight loss is resulted.

C) Initially without rent ceiling (corresponding to figure in part (A)):

Total consumer surplus = area of the green triangle = 1/2*1.6*(2500-2100) = $320 millions (using area of a right angled triangle: 1/2*base*height)

Total producer surplus = area of purple triangle = 1/2*1.6*(2100-1700) = $320 millions (again using the area of right angled triangle)

With rent ceiling, corresponding to the figure in part (B):

New consumer surplus = green area in below figure = ((2500-1900) + (2300 - 1900))*0.8/2 = $400 millions (using the area of a trapezium = (side 1 + side 2)*height/2)

New producer surplus = purple area in below figure = 1/2*0.8*(1900 - 1700) = $80 millions (using area of a right angled triangle).

Thus, change in consumer surplus = 400 - 320 = +$80 millions ('+' denoting increase)

And, change in producer surplus = 80 - 320 = -$240 millions ("-" denoting decrease)

Dead weight loss = area of grey triangle = (1/2)*(1.6 - 0.8)*(2300 - 1900) = $160 millions (sum of two right angled triangles).

So, we finally have:

In the presence of the rent control, consumers’ surplus increased by 80 million per month and producers’ surplus decreased by 240 million per month. The price ceiling on rent causes 60 million per month of dead weight loss.

D) Options (2), (3), and (4) are clearly incorrect, as we have already seen above that (1) not all consumers gain, as due to shortage, some consumers are unable to get a rented apartment. Only those, with very high willingness to pay are able to stay in the market. (2) Again, quantity of apartments have decreased, not increased, due to shortage, as already explained in the above parts. (3) There is no guarantee that quality of apartments will increase, in fact with lower rent, it might not be feasible to maintain the optimum quality of apartment.

First option is correct, this is the consequence of price/rent ceiling. Last option is also a possible one as some people who are left out of the market but in need of apartment might not get one. Thus, (1) and (5) shall be checked.