THIRD PART

Homework Question:

Model: y= 7x-40

The model is specified to be linear so we know that it will follow the formula of y=mx+b. We also know that the marginal cost is $7/unit. Since x is the # of units we know that 7x describes part of our cost. Meaning we now have y=7x+b. When we produce 20 items (when x = 20) our total cost is $100. This gives us 100= 7(20)+b. We can then solve for b and find that b=-40.

For 150 items our model predicts a cost of $1010. We find this by:

y=7(150)-40

y=1010

This means that the average cost per item increases as production levels increase. We find this through the following logic:

When we produced 20 items our cost was $100 (x=20, y=100) this means that the average cost per item was $5 (100/20). When we produced 150 items our cost was $1010 (x=150, y=1010) this means that the average cost per item was $6.73 (1010/150)

In consideration of other models, this model would be an example of one where average cost increases as production increases (as we have just shown.)

You obtain an economy of scale. This means that starting at some specific production level, the marginal cost is always less than the average cost.

Example: For every book that is purchased the price is going to be less than the overall (average) price of all the books. Eventually, the graph is going to intersect the average cost curve. But in our case that does not happen. Average cost is equal to total cost divided by the number of goods produced (the output quantity, Q). It is also equal to the sum of average variable costs (total variable costs divided by Q) plus average fixed costs (total fixed costs divided by Q).

The average cost diminishes as production increases- the slope in this case is negative, which means that the marginal cost is negative.