Arya\'s Pie Factory is a local bakery that specializes in pies and acts as a pri

Question

Arya's Pie Factory is a local bakery that specializes in pies and acts as a price taker. The prevailing price of a pie is $20. Arya's costs are given by C(q) - 0.15q5q + 500, where q represents the number of pie's that Arya's bake per day a. In order to maximize profit, how many pies should Arya's bake per day? How much profit does Arya's earn? b. Suppose the prevailing price is still $20. A salesman shows up at Arya's and offers to a new technology which would change Arya's cost function to C(a)- 0.05q+5q. How much should Arya's be willing to pay daily for this technology?

Explanation / Answer

a) As firm is price taker so there is perfectly competitive market. Equilibrium condition is P = MC.

MC = dTC/dq = 0.3q + 5

P = MC

20 = 0.3q + 5

0.3q = 15

q = 15/0.3 = 150/3 = 50 units

P = 20

Profit = TR - TC = P.q - 0.15q2 - 5q - 500 = 1000 - 375 - 250 - 500 = 1000 - 1125 = - $ 125

b) P = MC

20 = 0.1q + 5

20 - 5 = 0.1q

0.1q = 15

q = 15/0.1 = 150

q = 150 units

Profit = TR - TC = p.q - 0.05q2 - 5q = 3000 - 1125 - 750 = 3000 - 1875 = $ 1125

Arya would be willing to pay $ 1125 to earn normal profit.

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