# Probability: Are employment and economic trend independent?

Consider the following two economic characteristics with two possible outcomes each: employment (increase, decrease) and economic trend (positive, negative). Let the probability of a decreasing employment be 0.6 and the probability of a positive economic trend 0.5. Further, assume that the probability of a decreasing employment given a negative economic trend is 0.7.

Determine the probability of a positive economic trend given an increasing employment. Are employment and economic trend independent?

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#### Solution Preview

A competitive firm estimates its average variable cost function to be .

AVC=125-.21Q+.0007Q^2(squared)

The firm's total fixed cost is $3,500.

a. The marginal cost function associated with this average variable cost function is

SMC =__________________________.

a. The firm's total cost, TC = TFC +TVC

Or, TC = TFC + AVC.Q

Or, TC =3500 + (125 -0.21Q+ 0.0007Q2).Q

MC = d(TC)/dQ = 125 - 0.42Q + 0.0021Q2

b. AVC reaches its minimum at __150____ units of output. Minimum AVC is ___109.25______.

d(AVC)/dQ = o when AVC is at minimum

So, ...

#### Solution Summary

This solution helps with a probability problem regarding employment and economic trends.