Question

In: Economics

Behind the Supply Curve — End of Chapter Problem VC Quantity of trucks FC 20 orders...

Behind the Supply Curve — End of Chapter Problem

VC
Quantity of trucks FC 20 orders 40 orders 60 orders
2 $6,000 $2,000 $5,000 $12,000
3 7,000 1,800 3,800 10,800
4 8,000 1,200 3,600 8,400

Daniella owns a small concrete-mixing company. Her fixed cost is the cost of the concrete-batching machinery and her mixer trucks. Her variable cost is the cost of the sand, gravel, and other inputs for producing concrete; the gas and maintenance for the machinery and trucks; and her workers. She is trying to decide how many mixer trucks to purchase. She has estimated the costs shown in the accompanying table based on estimates of the number of orders that her company will receive per week.

a. For each level of fixed cost (i.e., for each number of mixer trucks), calculate Daniella's total cost of producing 20, 40, and 60 orders per week.

TC, 20 orders, 2 trucks: $

TC, 40 orders, 2 trucks: $

TC, 60 orders, 2 trucks: $

TC, 20 orders, 3 trucks: $

TC, 40 orders, 3 trucks: $

TC, 60 orders, 3 trucks: $

TC, 20 orders, 4 trucks: $

TC, 40 orders, 4 trucks: $

TC, 60 orders, 4 trucks: $

b. If Daniella is producing 20 orders per week, how many trucks should she purchase, and what will her average total cost be? Round average total cost to the nearest dollar.

Daniella should buy

  trucks.

Her average total cost will be $

per order.

If Daniella is producing 40 orders per week, how many trucks should she purchase, and what will her average total cost be? Round the average total cost to the nearest dollar.

Daniella should buy

  trucks.

Her average total cost will be $

per order.

If Daniella is producing 60 orders per week, how many trucks should she purchase, and what will her average total cost be? Round the average total cost to the nearest dollar.

Daniella should buy

  trucks.

Her average total cost will be $

per order.

Solutions

Expert Solution

(a). For each level of fixed cost i.e for each number of mixer trucks Daniella's total cost of producing 20, 40 and 60 orders per week is -

1) TC with 20 orders and 2 trucks : $6,000 (FC) + $2,000(VC) = $8,000.

2) TC with 40 orders and 2 trucks : $6,000(FC) + $5,000(VC) = $11,000.

3) TC with 60 orders and 2 trucks : $6,000 (FC) + $12,000(VC) = $18,000

4) TC with 20 orders and 3 trucks : $7,000(FC) + $1,800(VC) = $8,800.

5) TC with 40 orders and 3 trucks : $7,000 (FC) + $3,800(VC) = $10,800.

6) TC with 60 trucks and 3 trucks : $7,000 (FC) + $10,800(VC) = $17,800.

7) TC with 20 orders and 4 trucks : $8,000(FC) + $1,200(VC) = $9,200

8) TC with 40 orders and 4 trucks : $8,000(FC) + $3,600(VC) = $9,600

9) TC with 60 orders and 4 trucks : $8,000(FC) + $8,400(VC) = $16,400.

(b). If Daniella is producing 20 orders per week, then Daniella's cost with 2 trucks, 3 trucks and 4 trucks are $8,000 , $8,800 and $9,200. As Daniella will face lowest total cost if it has 2 trucks when order is 20 per week.

So, Daniella should purchase 2 trucks when order is 20 per week.

When Daniella's Total weekly cost is $8,000 with 20 orders per week then ATC (Avg Total cost) is $8,000/20 = $400 /order.

✓ If Daniella is producing 40 orders per week then Daniella's total cost with 2 trucks, 3 trucks and 4 trucks are $11,000 , $10,800 and $9,600.

As Daniella has lowest cost with 4 trucks when Daniella's order is 40 per week so Daniella should purchase 4 trucks. Total cost in case of 4 trucks with 40 orders per week is $9,600.

Daniella should buy 4 trucks when order is 40 per week.

Daniella's ATC will be $9,600/40 = $240/order.

✓ If Daniella is producing 60 orders per week then Daniella's total cost of production with 2 trucks, 3 trucks and 4 trucks are $18,000 , $17,800 and $16,400.

As Daniella has lowest cost with 4 trucks when it produces 60 orders per week. The total cost with 60 orders per week with 4 trucks is $16,400.

Daniella should buy 4 trucks when order is 60 per week.

Daniella's ATC will be $16,400/60 = $273.33/order.


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