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Consider the following table that describes the total cost of producing dresses by Shirley, a local fashion artist. Dresses Total cost ($)0 501 802 1053 1404 1805 2256 2757 350 Assume that the market is competitive and the price of dresses is $73. At this price how many dresses should Shirley produce to maximise profit? (If Shirley is indifferent between producing an additional dress and not producing, please assume that she will produce the additional dress to break the tie.)

Question

Consider the following table that describes the total cost of producing dresses by Shirley, a local fashion artist. Dresses Total cost ()050180210531404180522562757350 Assumethatthemarketiscompetitiveandthepriceofdressesis)0 501 802 1053 1404 1805 2256 2757 350 Assume that the market is competitive and the price of dresses is 73. At this price how many dresses should Shirley produce to maximise profit? (If Shirley is indifferent between producing an additional dress and not producing, please assume that she will produce the additional dress to break the tie.)

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Solution

To find out how many dresses Shirley should produce to maximize profit, we need to calculate the marginal cost of each dress and compare it with the market price of $73.

The marginal cost is the cost of producing one additional dress. It can be calculated by subtracting the total cost of producing n-1 dresses from the total cost of producing n dresses.

Here's the calculation:

  • The marginal cost of the first dress is 80−80 - 50 = $30.
  • The marginal cost of the second dress is 105−105 - 80 = $25.
  • The marginal cost of the third dress is 140−140 - 105 = $35.
  • The marginal cost of the fourth dress is 180−180 - 140 = $40.
  • The marginal cost of the fifth dress is 225−225 - 180 = $45.
  • The marginal cost of the sixth dress is 275−275 - 225 = $50.
  • The marginal cost of the seventh dress is 350−350 - 275 = $75.

Shirley should continue to produce dresses as long as the marginal cost is less than or equal to the market price. In this case, she should produce 7 dresses, because the marginal cost of the seventh dress (75)isslightlymorethanthemarketprice(75) is slightly more than the market price (73), but we assume that she will produce the additional dress to break the tie.

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