Explain step by step The market supply curve for a good is given by Q% = 1,000 +

Question

Explain step by step

The market supply curve for a good is given by Q% = 1,000 + 30P. The demand for the good can be segmented into two components. The first component is the demand by consumers of type A. This demand is given by q-^4 = 4,000 - 50P. The second component is the demand by consumers of type B. This demand is given by q^B = 4,500 - 10P. Derive the total market demand curve for the good. Show your work. (You may need to express the demand curve separately for different price ranges.) Find the equilibrium market price and quantity. Show your work and round to two decimal places as necessary.

Explanation / Answer

(a) Market Demad Curve = Demand by consumer type A + Demand by consumer type B

                               qM = qA + qB = 4000 - 50P + 4500 - 10P = 8500 - 60P

(b) For equilibrium we have to equate qM = qS

    => 8500 - 60P = 1000 + 30P

   => 90P = 7500

=> P = 7500 / 90 = $83.33 (equilibrium price)

and, q = 8500 - 60P = 8500 - 60(83.33) = 3500.2 (equilibrium quantity)

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