Profit Problem (need to maximize profit) and respective price elasticities

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2. A price-taking firm makes air conditioners. The market price of one of their new air conditioners is $120. Its total cost information is given in the following table.

Air conditioners/day ||||| Total cost($/day)

1 |||||||||||||||||||||||||||||||||||||||||||||||||||| 100

2 |||||||||||||||||||||||||||||||||||||||||||||||||||| 150

3 |||||||||||||||||||||||||||||||||||||||||||||||||||| 220

4 |||||||||||||||||||||||||||||||||||||||||||||||||||| 310

5 |||||||||||||||||||||||||||||||||||||||||||||||||||| 405

6 |||||||||||||||||||||||||||||||||||||||||||||||||||| 510

7 |||||||||||||||||||||||||||||||||||||||||||||||||||| 650

8 |||||||||||||||||||||||||||||||||||||||||||||||||||| 800



How many air conditioners should the firm produce per day if its goal is to maximize its profit?



8. What are the respective price elasticities of supply at A and B on the supply curve shown in the following figure?



http://i867.photobucket.com/albums/ab232/babymadphoto/pk6.jpg



Is it E=(△Q/Q)/(△P/P) ?

8. E=(3/9)/(2/6)

=1



I am afraid it's wrong

Thanks all for help.
 
1,101
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This is the wrong forum for asking such questions. Unfortunately I don't think there are any particularly well-known econ forums.

For 2, the firm is a price-taker, so we're assuming perfect competition here. In perfect competition, the price P is equal to Marginal Cost (MC), but you are given the market price, so you just need to find the marginal cost. Here the marginal cost is just the change in total cost since you're only given a discrete set of total costs. Thus all you need to do is figure out the change in total cost between 1 and 2 air conditioners, 2 and 3 air conditioners, and so on. Price might not exactly equal marginal cost, and even if it does, you need to remember that marginal cost is really "between" two successive units of quantity. But as long as the price P is greater than marginal cost, the marginal revenue will exceed marginal cost, so it is worth it for the firm to produce the extra unit. When P dips below marginal cost, it is no longer profitable to keep producing since the firm is losing money due to marginal cost being less than marginal revenue. Hence the firm will cut back. This is why P = MC is the profit maximization condition, but even if P cannot actually equal MC in this discrete case, this last bit of logic should help you figure out the optimal number of units the firm should produce.

As for 8, price elasticity can be calculated many ways. If you know some basic calculus, then that's probably the best way to go for determining elasticity at a point. Price elasticity would be (dQ/dP)(P/Q). Here (dQ/dP) is essentially the reciprocal of the slope of the given curve since price is a function of quantity. This allows you to evaluate the elasticity at a point.
 
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