1190 words - 5 pages

EEP1 Summer 2016

Problem Set 1

For full credit be sure to turn in your calculations.

The demand schedule (or demand function) for a good shows the total quantities (q) that buyers

are willing to buy at various alternative prices (p) in some period of time. For example, here is a

demand function illustrating the very special but convenient case of a linear demand (with q

measured in some physical unit of quantity such as bushels or tons and with p measured in

dollars per unit):

q = 2,100 -50p.

Sometimes it is convenient to express this in the inverse form showing the prices that buyers are

willing to pay for various quantities. This is called a demand-price function.

1. State the ...view middle of the document...

State the corresponding demand-price function, and plot it on your diagram, labeling it D2.

5. Determine the new equilibrium price:

p=

6. Suppose that consumers, indignant about this price increase, persuade their government to

institute price control and roll back the price to its former level. Distinguishing quantities

demanded and supplied by the superscripts d and s show that these differ:

qd =

qs =

7. Be prepared to discuss the following two statements:

"In a market where prices are determined by demand and supply, a price ceiling below the

unregulated equilibrium price helps consumers in one respect but hurts them in another."

"Prices are a device for rationing available supplies. If prices are prevented from discharging this

function, then the market must turn to some other form of rationing whether formal or informal,

orderly or disorderly."

II. The Case of Constant Cost

As another special case, assume that, in the long run, any relevant quantity of the good can be

produced at the constant cost of $18 per unit. (This unit cost is a "full cost," i.e., the minimum

cost per unit that producers must be able to cover if they are to be willing to go on producing

indefinitely.) This implies that the industry's supply-price function is given by:

p = 18.

8. Plot this on your diagram, labeling it S2, and note the equilibrium quantity (again using

demand curve D1) where demand price equals supply price:

q=

9. If the demand now increases as before to D2 (q = 2,700 -50p), calculate the new equilibrium

price and quantity:

p=

q=

10. If, alternatively, the government prevents this increase of output by requiring a license or

permit for each unit of output, how much will a license be worth per unit of output per period of

time if only the original output is allowed (How much would you pay for the right to produce a

unit?) Explain.

Value of license per unit of output per period =

III. The Case of Increasing Cost

As a somewhat more general case, assume that the supply function is positively sloped—though

still linear for convenience:

q = -600 + 100p where p > 6.

11. State the inverse of this function, i.e., the minimum prices that producers must receive if they

are to be willing to go on producing various alternative quantities:

p=

Supply curves may be positively sloped in the long run because, as the...

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