Consider the supply curves for a given firm in the market for gummy bears: qs = 2P-20. Assume that there are 10 identical gummy bear makers in the market. If the market demand for gummy bears is...

Consider the supply curves for a given firm in the market for gummy bears: qs = 2P-20. Assume that there are 10 identical gummy bear makers in the market. If the market demand for gummy bears is given by the following: P= 40 – 0.1QD, in the market equilibrium:

Quantity exchanged is equal to 20 and price is equal to 5

Quantity exchanged is equal to 50 and price is equal to 35

Quantity exchanged is equal to 200 and price is equal to 20

Quantity exchanged is equal to 100 and price is equal to 30

None of the above

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mathsworkmusic | (Level 2) Educator

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The market demand QD is the sum of the individual market supplies qs (these are equivalently individual market demands, since they are necessarily demanded by a set of consumers in a stable market).

We are told that there are 10 identical gummy bear makers, so that there are 10 equal individual market supplies/demands each equal to qs. Therefore we have the equation

QD = 10qs       (1)

We are given in the question that the individual market supply curves of the 10 gummy bear makers are defined by

qs = 2P - 20     (2)

where P is the global market price (variable) for a gummy bear.

Substituting (2) into (1) we obtain

QD = 10 x (2P - 20) = 20P - 200       (3)

In the question, we are also given that the market demand curve is defined by

P = 40 - 0.1QD                                   (4)

Now substituting (3) into (4) we obtain

P = 40 - 0.1 x (20P - 200) = 40 - 2P + 20 = 60 - 2P

Rearranging this gives

3P = 60     which implies that  the market price for a gummy bear is

P = 20

Substituting this into the equation for market demand QD in terms of P (equation 3), we get

QD = 20P - 200 = 400 - 200 = 200

So the quantity exchanged in a unit of time in the market is QD = 200 gummy bears (each of the ten firms sell 20 gummy bears), and these are exchanged at a price of P = 20 units of currency. So the answer is iii)

Sources:

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