Question

Consider a widget factory that uses both labor and capital in its production process. The cost of each worker is $12 per hour. The cost of each machine is $20 per hour, regardless of the number of widgets produced. The following table shows the production and cost structure of the firm, where L is the number of workers, K is the number of machines, and TP is the total product, measured in the number of widgets produced per hour.

L K TP MP FC VC TC AFC AVC ATC MC

0 2 0

1 2 20
2 2 35
3 2 45

4 2 50

5 2 53

6 2 55

(a) Calculate the firm’s marginal product of labor (MP), fixed cost (FC), variable cost (V C), total cost (TC), average fixed cost (AFC), average variable cost (AVC), average total cost (ATC), and marginal cost (MC) at each level of output. (7 points)

(b) For the range of output specified in the table, graph and explain the reasoning behind the shape of the firm’s production function and each of the following cost curves: TC, AFC, AV C, ATC, and MC. (9 points)

Answer 1

SHORT RUN PRODUCTION AND SHORT RUN COST

If you try to fill all the blanks in the table, your table should look like the next one. Note that I also added the formulas for each part of the table.

Because I'm using a european version please note that comas (,) are instead of decimal points.

• You can obtain average product by dividing total product by the total workers. This tells you in average, how much each worker produce.
• Marginal product is ho much the extra worker adds to total production. You calculate this by divinding the change in total production by the change in total workers.
• Fixed cost. because this is a short run production, capital is fixed (2). To obtain fixed cost you just multiplied capital cost (r = 20) by amount of capital (2).
• variable cost. The thing that changes in this chart is labor, that is your variable cost. Multiply labor by wage (12)
• Total Cost is the sum of fixed and variable cost
• Average variable cost is how much of variable cost are being designated for each item produce. You just need to divide total variable cost by the total production.
• Average fixed cost. divide total fixed cost by total output.
• Average total cost is the sum of average fixed cost and average variable cost.
• Marginal Cost. Marginal cost is how much producing the last item cost. You can obtain marginal cost by diving change in total cost by change in total product.

b)

In this case I used a online chart creator to create the next chart. Where AFC is in blue, AVC in red, ATC in purple and MC in organe.

• Fixed cost at first they go up and while production increases they fo down.
• AVC goes up while production goes up.
• ATC at first goes up and then goes down, after that, it increases but at a lower rate.
• MC Tends to fall and then goes up. this is because of the law of diminishing returns