Need help deriving the supply curve and the market supply/demand. Suppose that o

Question

Need help deriving the supply curve and the market supply/demand.

Suppose that on a Saturday night there are 20 people who'd each like pizza. Each person's willingness to pay for pizza is given by the equation W2Pi = 10-Qi where W2Pi is the maximum amount person i is willing to pay for pizza number Qi (eg. the person is willing to pay $9 for the first pizza, $8 for the second, etc.). There are 10 stores that will deliver a pizza. Each store has the following total cost equation: TCj=i6 + Qj*Qj, where Qj is the number of pizzas produced by firm j and Qj*Q j means Qj squared. The corresponding marginal cost equation is MCj=2*Qj. You may assume the market is perfectly competitive. Please answer the following questions. Derive the demand curve for a typical individual and the supply curve for a typical firm. Derive the market demand and supply curves. What is the equilibrium price and quantity of pizza? How many pizzas does each person buy? How much consumer surplus does each person receive? How many pizzas does each firm produce? How much profit does each firm earn?

Explanation / Answer

1.) Demand_Individual : Pi = 10-Qi

.....Supply _ firm : P =16+Qj*Qj - 2Qj

2.) Demand_market : Pi = 20*(10-Qi)

.....Supply Market : 10*(16+Qj*Qj - 2Qj)

3.) equating above two equations we get : Q = 2; P= 20*(10-2) = 160(Total)

4.) 3 pizzas (ie; 2 extras), 3 dollars,=(1+2)on each extra pizza

5.) Each firm Produces 2 pizza : 10*(16+Qj*Qj - 2Qj) = 160 => Qj = 2

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