Question

Suppose there are two groups in the economy who demand fidget spinners with the aggregate demand for rapid spinners being P = 40−2×Q^R_D and the aggregate demand for slow spinners being P = 20 − 2 × Q^S_D.

If there are 10 rapid spinners and 20 slow spinners in the economy what is the individual demand function of a single member of each group?

Find the market demand function. Suppose the (inverse) supply function for fidget spinners is P = 4 + 2 × Q. What is the equilibrium price and quantity here? Do both groups buy fidget spinners?

Suppose the government feels that fidget spinners do an excellent job of reducing stress and want more people to have fidget spinners. This can be accomplished if the government subsidies them (a subsidy can be viewed as a negative tax). Suppose the government gives a $10 per fidget spinner subsidy to the producers, what is the new market price and quantity? How much does the subsidy cost the government?

Answer 1

1. given Aggregate demand for fidget spinners is

P = 40-2QRD and Aggregate demand for slow spinners is P = 20- 2QSD

Also no. of rapid spinners = 10 and no. of slow spinners = 20,

therefore, individual demand for fidget spinners is

P/10 = 4 - QRD/5 (Dividing either side by no. of rapid spinners ie., 10)

Also individual demand for slow spinners is

P/20 = 1- QSD/10 (Dividing either side by no. of slow spinners i.e., 20)

Also total quantiity demanded Q = QRD +QSD

Therefore, market demand function is, aggregate demands of both rapid spinners and slow spinners or,

P = (40-2QRD + 20 -2QSD) =60- 2(QRD+QSD) = 60-2Q

or, P = 60-2Q ......(i)

2. Given inverse supply function is,

P = 4 +2Q ......(ii)

Under equilibrium market condition,

Demand = Supply

Therefore, 60-2Q = 4 +2Q

or 4Q = 56 i.e., Q =14 Therefore equilibrium quantity = 14

Therefore, equilibrium price = 60-2Q = 60- 2*14 = 32

Here, Q = QRD +QSD or, QRD +QSD =14

or, QRD = 14-QSD

Putting the value of QRD in the aggregate demnd function of fidget spinners, we get,

P = 40 -2(14-QSD) or, P = 40-28+2QSD or P = 12+2QSD

Under equilibrium market condition,

Aggregate demnd of both spinners must be same

i.e., 12 +2QSD = 20-2QSD

or 4QSD = 8 or, QSD = 2 and QRD = 14-QSD= 14-2 =12

Therefore, each group buys separate spinners.

3. If government offers $10 per fidget spinner subsidy to the fidget spinners producers, then new aggreggate market demand function will be,

P= 40-2(QRD -10) (Replacing QRD with QRD-10 because any subsidy to the item will reduce the price of that item)

or P = 60-2QRD.......(iii)

and Aggregate demand for slow spinners is P = 20-2QSD.....(iv)

Adding (iii) and (iv), we get market demand or P = 60-2QRD +20-2QSD

or P = 80-2Q

Also inverse supply fuunction or P = 4+2Q

Under equilibrium state,

market demand = market supply

or, 80-2Q = 4+2Q or, 4Q=76 or Q =19

Also P = 4 +2Q = 4+2.19 = 42

Putting value of P in aggregate demand for slow spinners,

we get 42 = 60-2QRD, or, QRD = 9

Also Q = QRD +QSD

or QRD +QSD = 19

For maximum utilization of fidget spinners, no. of slow spinners or QSD = 0, Therefore no. of fidget spinners

therefore, total subsidy cost of the government = subsidy rate * no.of fidget spinners = $10 * 19 = $190