Suppose you are in the retail business of selling designer pens. If you set the

Question

Suppose you are in the retail business of selling designer pens. If you set the price at $12 per pen, you can sell 45 pens. If you set the price at $20 per pen, you can sell 5 pens. On the other hand, your supplier is prepared to sell you 135 pens at a price of $18, and 79 pens at a price of $10. Find the corresponding supply and demand equation. What is the equilibrium price?

Explanation / Answer

assuming supply and demand to be linear let p=aq+b => 12 = 45a + b -------------(1) and 20 = 5a + b ----------------------(2) solving (1) and (2) gives a = -0.2 and b=21 thus demand equation is p = 21 - 0.2q where p is price and q is quantity for supply equation s = aq+b => 18 = 135a + b ---------------(3) and 10 = 79a + b --------------(4) solving (3) and (4) gives a = 0.14286 and b = -1.2857 thus supply equation is s = 0.14286q - 1.2857 for equilibrium s = p => 21 - 0.2q = 0.14286q - 1.2857 => q = 64.9999 = 65 thus equilibrium price is price for q = 65 i.e equilibrium price = $8 Ans

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