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Q: Economics ( Answered,   0 Comments )
Question  
Subject: Economics
Category: Business and Money > Economics
Asked by: douger-ga
List Price: $5.00
Posted: 02 Jul 2003 21:24 PDT
Expires: 01 Aug 2003 21:24 PDT
Question ID: 224585
A firm has fixed costs of $500 per month and its marginal cost is MC=
$10.00*Q
Show table of quantity, total cost, average total cost, marginal cost,
total variable cost, average variable cost for the first 10 units of
output.

Facing a price of $100.00, what is the quantity at which the firm will
break even?
Estimate the elasticity of cost with respect to output.
Answer  
Subject: Re: Economics
Answered By: wonko-ga on 03 Jul 2003 23:31 PDT
 
Quantity Total Cost Average Total Cost Marginal Cost Total Variable
Cost Average Variable Cost

1	510	510.00	10	10	10
2	520	260.00	20	20	10
3	530	176.67	30	30	10
4	540	135.00	40	40	10
5	550	110.00	50	50	10
6	560	93.33	60	60	10
7	570	81.43	70	70	10
8	580	72.50	80	80	10
9	590	65.56	90	90	10
10	600	60.00	100	100	10

Marginal cost is the only variable cost present, so that is why
marginal cost and total variable cost are the same.

The breakeven quantity if the price is $100 each is 6 (Revenue equal
$600, Total Cost equals $560, profit equals $40).

As larger numbers of units are produced, the elasticity of cost with
respect to output approaches one.  This is because the fixed cost per
unit approaches zero as the number of units increases, resulting in a
linear relationship between total cost and quantity produced. 
Elasticity is computed by the formula Delta Q/(Q1 + Q2)/2/Delta
TC/(TC1 + TC2).  Elasticity is defined as the percentage change in
Total Cost for every 1% change in output quantity.

The elasticity of cost between the production of 1 unit and 2 units is
34.33.  The elasticity of cost between the production of 9 units and
10 units is 6.26.  The elasticity of cost between the production of
9,999 units and 10,000 units is 1.05.  The elasticity of cost between
the production of 999,999 and one million units is 1.00005.

Sincerely,

Wonko

Request for Answer Clarification by douger-ga on 05 Jul 2003 09:16 PDT
Can you show more detail in the last question relating to elasticity
of cost, for example plug in the numbers to show the elasticity of
cost with respect to output of 5 to 6 units.

Clarification of Answer by wonko-ga on 05 Jul 2003 12:57 PDT
Sure.  The elasticity of costs with respect to output for the output
of five to six units is 10.09.  It is calculated using the formula
Delta Q/(Q1 + Q2)/2/Delta TC/(TC1 + TC2)/2.

The change in Q is one (six minus five).  The average of the two
quantities is 5.5 (the quantity six plus five divided by two).  The
change in P is 10 (560 -550).  The average of the two prices is 555
(the quantity 550 plus 560 divided by two).  The elasticity is
calculated by the change in Q/the average of the two quantities/the
change in P/the average of the two prices = 1/5.5/10/555 = 10.09.

I hope this clarifies things for you.

Sincerely,

Wonko
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