This problem deals with the effects of a price control (or a price ceiling). Sup

Question

This problem deals with the effects of a price control (or a price ceiling). Suppose that the market demand curve is given by P 6- (1/1000)Q and that the market supply curve is given by P 1+ (1/1000)a. Note that, in doing the calculations below, it's easier to leave the (1/1000) factors as is without converting to a decimal a) Set the P values equal using the above formulas, and solve for the equilibrium quantity in the market. This quantity is given bySubstituting this solution back into the demand function, the equilibrium price is P(put two digits after the decimal point), Suppose that the market demand comes from adding up the demands of 1000 identical consumers. Using the above Q solution, individual consumption at the market equilibrium is equal tounits (put one digit after the decimal point). b) Now suppose the government institutes a price control, setting the price of the good at P 2. At this price, the quantity supplied equals units (set P 2 in the supply formula and solve for Q). The quantity demanded equals units (set P 2 in the demand formula and solve for Q). With 1000 consumers, each individual's desired purchase is then equal to units c) Excess demand in the market is equal tounits, so that everyone's consumption desires cannot be satisfied. Suppose that consumers get in line to buy the good, with consumers buying their desired quantity unti the good runs out. Using the answers from part (b), you can conclude that consumers get to purchase their desired quantity, while consumers get nothing (these are the people still in line when the supply runs out)

Explanation / Answer

(a) Market demand, P= 6- (1/1000)Q

Market supply ,P=1+(1/1000)Q

For equilibrium equate demand and supply :

6- (1/1000)Q = 1+(1/1000)Q

5=2Q /1000

Q = 5000/2

Q = 2500 units (equilibrium quantity)

Equilibrium price ,P = 6- (1/1000)Q (put the value of Q in this) ,

P = 6 - (1/1000)2500

P= 6 -2.5

P= $ 3.5 (equilibrium price)

Now, individual consumption at the market equilibrium isn equal to (2500/1000) = 2.5 units.

(b) When the price ceiling is P=$2 .Then, Quantity supplied , P=1+ (1/1000)Q

Put P= 2 in this market supply equation then, 2 = 1+(1/1000)Q

QS = 1000 units

When the price ceiling is P=$2 .Then, Quantity demanded , P= 6- (1/1000)Q

Put P= $2 in this market demand equation the, 2 = 6- (1/1000)Q

QD = 4000 units.

With 1000 consumers ,each individual's desired purchase is then equal to 4000/1000 = 4 units.

(c) Excess demand in themarket is equal to (QD -QS) = (4000- 1000)= 3000 units,so that everyone's consumption idesires is not satisfied. Suppose that consumers get in line to buy the good , with consumers buying their quantity the goods runds out.We can conclude that (1000/4) = 250 consumers get to purchase their desired quantity , while (1000-250 )=750 consumers get nothing. Because after 250 customers supply runs out i.e (250)(4)=1000 units which is equal to quantity supplied.

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